~ 1 ~
V. EMPIRICAL RESULTS
V.1. DESCRIPTIVE STATISTICS
For each of the market returns, the descriptive statistics and their corresponding
standard errors and test statistics are calculated using Excel. The results for the first and
second moments for total observations are arranged on regional classification and
presented in the following table:
SIZE MEAN MAX MIN MEDIAN STD. DEV
EGYPT 495 0.0004- 0.0240 0.0538- 0.0010 0.0104
ISRAEL 546 0.0002 0.0340 0.0566- 0.0012 0.0114
S. AFRICA 675 0.0001- 0.1003 0.1138- 0.0010 0.0189
ARGENTINA 647 0.0009- 0.0653 0.1052- 0.0005 0.0157
BRAZIL 733 0.0008 0.1231 0.1124- 0.0019 0.0223
CANADA 698 0.0005- 0.0815 0.0892- 0.0009 0.0147
CHILE 662 0.0004 0.1060 0.0698- 0.0019 0.0133
MEXICO 669 0.0000 0.0850 0.0860- 0.0011 0.0173
UNITED STATES 733 0.0003- 0.0689 0.0689- 0.0003 0.0122
AUSTRALIA 712 0.0001- 0.0831 0.0804- 0.0013 0.0157
CHINA 657 0.0016 0.0865 0.0548- 0.0029 0.0153
HONG KONG 651 0.0002 0.0759 0.1049- 0.0010 0.0149
INDONESIA 634 0.0000 0.0662 0.1033- 0.0017 0.0157
INDIA 632 0.0003 0.0609 0.0806- 0.0017 0.0166
JAPAN 632 0.0005- 0.0786 0.0591- 0.0000 0.0121
MALAYSIA 646 0.0001- 0.0288 0.0536- 0.0006 0.0090
NEW ZEALAND 688 0.0005- 0.0569 0.0548- 0.0004 0.0121
PHILIPPINES 649 0.0000- 0.0508 0.0776- 0.0015 0.0145
SINGAPORE 678 0.0004- 0.0526 0.0639- 0.0006 0.0123
S. KOREA 644 0.0006 0.1378 0.1139- 0.0018 0.0189
TAIWAN 650 0.0002- 0.0565 0.0454- 0.0011 0.0123
THAILAND 624 0.0003- 0.0575 0.0874- 0.0001 0.0124
AFRICA
AMERICA
ASIA
~ 2 ~
SIZE MEAN MAX MIN MEDIAN STD. DEV
EURO AREA 717 0.0002- 0.0727 0.0701- 0.0003 0.0140
AUSTRIA 662 0.0006- 0.1097 0.0821- 0.0008 0.0178
DENMARK 693 0.0004- 0.0757 0.0682- 0.0005 0.0147
FRANCE 718 0.0002- 0.0767 0.0715- 0.0006 0.0142
GERMANY 714 0.0001 0.0755 0.0649- 0.0011 0.0139
NETHERLANDS 715 0.0004- 0.0717 0.0740- 0.0005 0.0147
RUSSIA 647 0.0000 0.1484 0.1310- 0.0011 0.0219
SPAIN 711 0.0001 0.0733 0.0685- 0.0011 0.0139
SWEDEN 689 0.0001- 0.0852 0.0674- 0.0012 0.0165
SWITZERLAND 693 0.0003- 0.0760 0.0577- 0.0003 0.0114
UNITED KINGDOM 711 0.0005- 0.0785 0.0709- 0.0003 0.0139
EUROPE
Table 1. Descriptive Statistics of the Full Sample Market Returns based on Regional Classification
From the table above it can be seen that several economies have positive average
returns: Israel, Brazil, Chile, Mexico, China, Hong Kong, Indonesia, India, South Korea,
Germany, and Spain. As for the rest of the markets, they reported negative average return.
Nevertheless, the median for all markets are uniformly positive. It signifies the presence of
extreme large values in the distribution. As for the variation around the mean return,
Russia shows the highest volatility during the time period considered. Volatility is highest in
South Africa, Brazil, South Korea and Russia for Africa, America, Asia, and Europe region,
respectively. Since the samples are divided into two sub-groups, the statistics of each
period are also determined and summarized as follows1:
1 Since the lag order p = 3, observation for tranquil period starts at t = p + 1 = 4
~ 3 ~
SIZE MEAN MAX MIN MEDIAN STD. DEV
EGYPT 472 0.0002- 0.0240 0.0538- 0.0010 0.0101
ISRAEL 546 0.0002 0.0340 0.0566- 0.0011 0.0114
S. AFRICA 675 0.0002- 0.1003 0.1138- 0.0009 0.0190
ARGENTINA 554 0.0004- 0.0589 0.0524- 0.0006 0.0117
BRAZIL 623 0.0012 0.0842 0.0774- 0.0020 0.0172
CANADA 595 0.0001 0.0556 0.0525- 0.0010 0.0099
CHILE 559 0.0008 0.0354 0.0415- 0.0018 0.0102
MEXICO 568 0.0006 0.0582 0.0412- 0.0017 0.0123
UNITED STATES 626 0.0000 0.0490 0.0459- 0.0005 0.0077
AUSTRALIA 605 0.0004 0.0720 0.0552- 0.0014 0.0116
CHINA 556 0.0017 0.0865 0.0548- 0.0029 0.0151
HONG KONG 551 0.0006 0.0565 0.0417- 0.0012 0.0113
INDONESIA 547 0.0007 0.0537 0.0678- 0.0023 0.0135
INDIA 548 0.0010 0.0534 0.0575- 0.0021 0.0144
JAPAN 543 0.0001- 0.0295 0.0282- 0.0001 0.0089
MALAYSIA 558 0.0002 0.0276 0.0536- 0.0008 0.0084
NEW ZEALAND 585 0.0000- 0.0346 0.0477- 0.0005 0.0089
PHILIPPINES 546 0.0004 0.0475 0.0572- 0.0018 0.0126
SINGAPORE 578 0.0004 0.0344 0.0407- 0.0010 0.0098
S. KOREA 541 0.0009 0.0407 0.0355- 0.0019 0.0109
TAIWAN 552 0.0000- 0.0444 0.0454- 0.0011 0.0104
THAILAND 526 0.0003 0.0373 0.0874- 0.0003 0.0108
EURO AREA 608 0.0002 0.0467 0.0391- 0.0003 0.0090
AUSTRIA 560 0.0001- 0.0679 0.0649- 0.0008 0.0120
DENMARK 586 0.0003 0.0463 0.0559- 0.0011 0.0102
FRANCE 609 0.0002 0.0486 0.0404- 0.0007 0.0094
GERMANY 607 0.0005 0.0356 0.0383- 0.0011 0.0089
NETHERLANDS 607 0.0001- 0.0432 0.0712- 0.0006 0.0099
RUSSIA 553 0.0003 0.1172 0.0893- 0.0011 0.0158
SPAIN 604 0.0006 0.0486 0.0368- 0.0014 0.0090
SWEDEN 584 0.0002 0.0509 0.0535- 0.0013 0.0112
SWITZERLAND 586 0.0001 0.0324 0.0356- 0.0004 0.0078
UNITED KINGDOM 602 0.0000- 0.0514 0.0467- 0.0005 0.0091
AFRICA
AMERICA
ASIA
EUROPE
Table 2. Descriptive Statistics of Market Returns for Tranquil Period
~ 4 ~
SIZE MEAN MAX MIN MEDIAN STDEV
EGYPT 20 0.0057- 0.0121 0.0340 0.1003 0.0153
ISRAEL 35 0.0010- 0.0445- 0.0566- 0.1138- 0.0220
S. AFRICA 104 0.0016- 0.0035- 0.0034 0.0026- 0.0353
ARGENTINA 90 0.0048- 0.0653 0.1052- 0.0033- 0.0304
BRAZIL 107 0.0017- 0.1231 0.1124- 0.0003- 0.0411
CANADA 100 0.0041- 0.0815 0.0892- 0.0029- 0.0302
CHILE 100 0.0018- 0.1060 0.0698- 0.0024 0.0243
MEXICO 98 0.0033- 0.0850 0.0860- 0.0051- 0.0341
UNITED STATES 107 0.0022- 0.0689 0.0689- 0.0028- 0.0261
AUSTRALIA 104 0.0032- 0.0831 0.0804- 0.0016- 0.0302
CHINA 98 0.0011 0.0450 0.0424- 0.0003 0.0170
HONG KONG 97 0.0020- 0.0759 0.1049- 0.0000- 0.0278
INDONESIA 84 0.0047- 0.0662 0.1033- 0.0039- 0.0256
INDIA 81 0.0040- 0.0609 0.0806- 0.0025- 0.0272
JAPAN 86 0.0033- 0.0786 0.0591- 0.0060- 0.0239
S. KOREA 100 0.0011- 0.1378 0.1139- 0.0023- 0.0409
MALAYSIA 85 0.0017- 0.0288 0.0300- 0.0030- 0.0123
NEW ZEALAND 100 0.0031- 0.0569 0.0548- 0.0008- 0.0232
PHILIPPINES 100 0.0023- 0.0508 0.0776- 0.0002- 0.0221
SINGAPORE 97 0.0049- 0.0526 0.0639- 0.0039- 0.0214
TAIWAN 95 0.0013- 0.0565 0.0418- 0.0009 0.0199
THAILAND 95 0.0038- 0.0575 0.0579- 0.0032- 0.0188
EURO AREA 106 0.0025- 0.0727 0.0701- 0.0021- 0.0292
AUSTRIA 99 0.0035- 0.1097 0.0821- 0.0042- 0.0362
DENMARK 104 0.0041- 0.0757 0.0682- 0.0033- 0.0290
FRANCE 106 0.0023- 0.0767 0.0715- 0.0020- 0.0292
GERMANY 104 0.0022- 0.0755 0.0649- 0.0020- 0.0294
NETHERLANDS 105 0.0025- 0.0717 0.0740- 0.0016- 0.0301
RUSSIA 91 0.0020- 0.1484 0.1310- 0.0008 0.0435
SPAIN 104 0.0026- 0.0733 0.0685- 0.0031- 0.0290
SWEDEN 102 0.0026- 0.0852 0.0674- 0.0019- 0.0290
SWITZERLAND 104 0.0027- 0.0760 0.0577- 0.0020- 0.0228
UNITED KINGDOM 106 0.0031- 0.0785 0.0709- 0.0021- 0.0286
AFRICA
AMERICA
EUROPE
ASIA
Table 3. Descriptive Statistics of Market Returns for Turmoil Period
~ 5 ~
In tranquil times, there are only a handful of markets exhibit negative mean
returns: Egypt, South Africa, Argentina, Japan, New Zealand, Taiwan, Austria, the
Netherlands and United Kingdom. However, during the turmoil period, all markets
uniformly reported negative average return. The opposite direction is observed in the
variance of each return, the volatility is significantly higher during the turmoil period. This
pattern is omnipresent for all markets under investigation.
In order to deduce information from the distribution of the market returns, these
statistics are analysed using parametric tests described in details in the preceding chapter.
The standard error and t-statistic for each distribution parameters mentioned above are
calculated only for the full sample. The results are arranged based on regional
classification:
~ 6 ~
STAT SE t STAT SE t STAT SE t
EGYPT 0.00- 0.00 0.87- 1.07- 0.11 9.72- 2.48 0.22 2.37-
ISRAEL 0.00 0.00 0.51 1.00- 0.10 9.57- 3.40 0.21 1.88
S. AFRICA 0.00- 0.00 0.17- 0.02 0.09 0.22 4.67 0.19 8.87
ARGENTINA 0.00- 0.00 1.51- 0.85- 0.10 8.79- 6.10 0.19 16.10
BRAZIL 0.00 0.00 0.92 0.13- 0.09 1.42- 5.05 0.18 11.34
CANADA 0.00- 0.00 0.88- 0.62- 0.09 6.64- 7.96 0.19 26.75
CHILE 0.00 0.00 0.83 0.22- 0.10 2.36- 9.05 0.19 31.80
MEXICO 0.00 0.00 0.05 0.21- 0.09 2.26- 5.06 0.19 10.85
UNITED STATES 0.00- 0.00 0.67- 0.30- 0.09 3.37- 7.04 0.18 22.34
AUSTRALIA 0.00 0.00 0.16- 0.02 0.10 3.86- 1.89 0.19 11.47
CHINA 0.00 0.00 2.68 0.12- 0.10 0.16 6.78 0.19 5.82-
HONG KONG 0.00 0.00 0.30 1.10- 0.10 1.23- 6.45 0.19 19.71
INDONESIA 0.00 0.00 0.01 0.52- 0.10 11.27- 2.22 0.19 17.73
INDIA 0.00- 0.00 0.51 0.15- 0.10 5.35- 5.44 0.19 4.02-
JAPAN 0.00- 0.00 1.05- 0.60- 0.10 1.52- 3.42 0.19 12.52
MALAYSIA 0.00- 0.00 0.17- 0.56- 0.09 6.22- 3.98 0.19 2.17
NEW ZEALAND 0.00- 0.00 1.07- 0.58- 0.10 6.03- 3.19 0.19 5.25
PHILIPPINES 0.00- 0.00 0.03- 0.49- 0.09 6.06- 3.52 0.19 0.96
SINGAPORE 0.00 0.00 0.83- 0.15 0.10 5.17- 14.44 0.19 2.77
S. KOREA 0.00- 0.00 0.81 0.26- 0.10 1.60 1.62 0.19 59.28
TAIWAN 0.00- 0.00 0.37- 0.76- 0.10 2.69- 6.80 0.20 7.20-
THAILAND 0.00- 0.00 0.63- 0.76- 0.10 7.80- 6.80 0.20 19.39
EURO AREA 0.00- 0.00 0.35- 0.01 0.09 0.07 5.53 0.18 13.84
AUSTRIA 0.00- 0.00 0.89- 0.04- 0.10 0.44- 6.78 0.19 19.87
DENMARK 0.00- 0.00 0.66- 0.38- 0.09 4.05- 5.95 0.19 15.83
FRANCE 0.00- 0.00 0.33- 0.19 0.09 2.05 6.08 0.18 16.84
GERMANY 0.00 0.00 0.18 0.07 0.09 0.72 5.58 0.18 14.07
NETHERLANDS 0.00- 0.00 0.75- 0.33- 0.09 3.65- 5.84 0.18 15.51
RUSSIA 0.00 0.00 0.03 0.13- 0.10 1.38- 11.47 0.19 43.97
SPAIN 0.00 0.00 0.22 0.11- 0.09 1.22- 6.18 0.18 17.32
SWEDEN 0.00- 0.00 0.09- 0.18 0.09 1.92 4.37 0.19 7.33
SWITZERLAND 0.00- 0.00 0.70- 0.07- 0.09 0.73- 6.22 0.19 17.32
UNITED KINGDOM 0.00- 0.00 0.96- 0.10 0.09 1.03 7.31 0.18 23.43
AFRICA
AFRICA
ASIA
EUROPE
KURTOSISMEAN SKEWNESS
Table 4. Distribution Parameter Test Statistics based on Regional Classification
At level of significance α = 5% the null hypothesis of the sample means cannot be
rejected for almost all stock markets considered in this study. The parametric test
~ 7 ~
conducted on the sample mean indicates the estimated arithmetic mean is significant for
most of the countries investigated, except for the Shanghai SE in China. The t-statistic
indicates that we reject the null hypothesis for this market.
The second parametric test is carried out on the skewness coefficient. The results
of the test for skewness indicate that the distribution of international equity market
encompasses different shapes. Some estimated skewness coefficients are not significantly
different from zero; this is the case for market returns in South Africa, Brazil, China, Hong
Kong, Japan, South Korea, Euro Area, Austria, Germany, Russia, Spain, Sweden, Switzerland
and United Kingdom. As for the sample from Egypt, Israel, Argentina, Canada, Chile,
Mexico, United States, Australia, Indonesia, India, Malaysia, New Zealand, Philippines,
Singapore, Taiwan, Thailand, Denmark and the Netherlands, the null hypothesis is rejected
and the estimated negative coefficient of skewness for each of these market is statistically
significant. It is worth nothing that Indonesia has the highest negative skewness coefficient.
On the other hand, only one market shows a significant positively-skewed distribution, i.e.
the CAC 40 in France.
Random variables with a negative skewness coefficient is said to have a distribution
that is distorted to the left, i.e. left-skewed, due to the presence of extremely small values
(Berenson, Levine, & Krehbiel, 2009). In other words, this distribution is characterized by
higher probability for values to be lower than the expected value that it is for value to fall
above the mean (Hamilton, 1994). Since most of the values are in the upper proportion of
the distribution, the mean value of this distribution is smaller than its median (Berenson,
Levine, & Krehbiel, 2009).
Contrarily, a positive value of skewness coefficient indicates right-skewness which
means that the mean are larger than the median, i.e. most of the values are in the lower
~ 8 ~
proportion of the distribution (Berenson, Levine, & Krehbiel, 2009). The result of the t-test
indicates the presence of extreme positive values, i.e. higher returns than expected, in
France market.
The third test implemented in this study is the test of excess kurtosis. Test statistics
for kurtosis coefficient reveal that most of the returns in this study have significant positive
excess kurtosis (Kr > 3). This type of distribution is said to have high peak and heavy tails,
and often referred to as a leptokurtic distribution (Tsay, 2005). This type of distribution
implies that the tails of its support have more mass than a Gaussian distribution with the
same variance does (Hamilton, 1994; Tsay, 2005). In practice, this means that a random
sample from such a distribution tends to contain more extreme values from the upper or
the lower side of the mean (Tsay, 2005).
Only two countries are found to have kurtosis coefficient not significantly different
from three, i.e. Israel and the Philippines. Therefore, it can be conjectured that the peak
and tails of the distribution from the two markets are approaching those of normal
distribution. On the other hand, some countries, namely Egypt, China, India, and Taiwan,
are found to have kurtosis coefficient to be significantly less than three. Distribution with
negative excess kurtosis has short tails and is called a platykurtic distribution (Tsay, 2005).
This type of distribution will be less peaked in the mean, have thinner tails and more of the
distribution in the shoulders than a normal distribution (Brooks, 2008).
Countries in this study are also grouped according to their income level (The World
Bank, 2010). Classifying countries based on their economic development provides another
perspective on the distribution of market returns. Therefore the results are re-arranged as:
~ 9 ~
COUNTRY SKEWNESS KURTOSIS COUNTRY SKEWNESS KURTOSIS
CHINA NON PLATY CANADA NEGATIVE LEPTO
EGYPT NEGATIVE PLATY DENMARK NEGATIVE LEPTO
INDONESIA NEGATIVE LEPTO EURO AREA NON LEPTO
INDIA NEGATIVE PLATY FRANCE POSITIVE LEPTO
PHILIPPINES NEGATIVE NON GERMANY NON LEPTO
THAILAND NEGATIVE LEPTO HONG KONG NON LEPTO
ISRAEL NEGATIVE NON
ARGENTINA NEGATIVE LEPTO JAPAN NON LEPTO
BRAZIL NON LEPTO NETHERLANDS NEGATIVE LEPTO
CHILE NEGATIVE LEPTO NEW ZEALAND NEGATIVE LEPTO
MALAYSIA NEGATIVE LEPTO SINGAPORE NEGATIVE LEPTO
MEXICO NEGATIVE LEPTO S. KOREA NON LEPTO
RUSSIA NON LEPTO SPAIN NON LEPTO
S. AFRICA NON LEPTO SWEDEN NON LEPTO
SWITZERLAND NON LEPTO
AUSTRALIA NEGATIVE LEPTO UNITED KINGDOM NON LEPTO
AUSTRIA NON LEPTO UNITED STATES NEGATIVE LEPTO
LOWER-MIDDLE INCOME
UPPER-MIDDLE INCOME
HIGH INCOME
HIGH INCOME
Table 5. Distribution Parameters based on Income-Level Classification2
The results in Table 6. indicate that all of the countries in lower-middle income
group, except for China, have significant negatively-skewed distribution. For other income
levels the results indicate a rather heterogeneous picture: some markets have left-skewed
distribution; some do not have significant skewness in their distribution. One market in
high-income group exhibits positively-skewed distribution. However, the analysis of
kurtosis coefficients when countries are grouped based on their economic development
indicates a somewhat regular pattern. Other than Israel, all of the countries in the upper-
middle and high income groups have significant leptokurtic distribution. Meanwhile only
two countries in the lower-middle income group exhibit significant excess kurtosis. These
statistics appear to be in contrary to the results obtained by another study in international
stock markets over the period of 1994 - 2005 (Evans & McMillan, 2009) in which they
suggested that excess kurtosis is more noticeable for developing economies.
2 Taiwan is excluded from the list based on income-level classification because it is not listed on the
World Bank website
~ 10 ~
V.2. NORMALITY TEST
EGYPT 100.19 NEW ZEALAND 63.90
ISRAEL 95.05 PHILIPPINES 37.69
S. AFRICA 78.81 SINGAPORE 34.37
S. KOREA 3,516.51
ARGENTINA 336.49 TAIWAN 59.10
BRAZIL 130.54 THAILAND 436.77
CANADA 759.85
CHILE 1,016.71 EURO AREA 191.54
MEXICO 122.87 AUSTRIA 394.88
UNITED STATES 510.26 DENMARK 267.14
FRANCE 287.79
AUSTRALIA 146.56 GERMANY 198.35
CHINA 33.95 NETHERLANDS 253.96
HONG KONG 389.89 RUSSIA 1,935.69
INDONESIA 441.17 SPAIN 301.52
INDIA 44.86 SWEDEN 57.39
JAPAN 159.04 SWITZERLAND 300.46
MALAYSIA 43.42 UNITED KINGDOM 550.20
AFRICA ASIA
AMERICA
EUROPE
ASIA
Table 6. Normality Test of Market Returns
From the results of the JB statistics tabulated in Table 7, it can be concluded that all
of stock returns in this study are found to have a distribution which is significantly different
from normal distribution, with South Korea have the highest JB statistic. Non-normality in
financial data could correspond to a one-off or extreme events that are unlikely to be
repeated and the information content of which is deemed of no relevance for the data as a
whole (e.g. stock market crashes, financial panics, etc) or it could also arise from certain
types of heteroscedasticity (Brooks, 2008) whereas in the latter case the non-normality is
intrinsic to all of the data and outlier removal would not make the residuals of such a
model normal.
No conclusion can be made regarding the source of the non-normality of market
returns examined in this study. However, it is worth noting that a leptokurtic distribution
~ 11 ~
with fatter tails and is more peaked at the mean than a normally distributed random
variable with the same mean and variance is far more likely to characterize financial time
series and the residuals from a financial time series model (Tsay, 2005; Brooks, 2008). The
larger the deviation from normality for market returns, the more volatile they are, i.e.
extreme values can be observed with relatively higher frequency.
It is suggested that positive kurtosis and negative skewness can be attributed to
not only the inherent heteroscedasticity of market returns, i.e. time-varying variance, but
also to the non-stationarity of their population mean, as appear to be the case of this study
(Fama, 1965; Stokie, 1982). As the result of the unconditional heteroscedasticity, even for a
very large sample the variability of the sample variance will not tend to dampen nearly as
much as would be expected with a Gaussian process (Fama, 1965). Nevertheless, due to
the scope of this study, implications of the non-normality in market returns are assumed
away.
On the other hand, the normality of the distribution of the error terms, i.e.
regression residuals, , is necessary for this study. The exact normality of the
OLS estimators is hinged crucially on the normality of the distribution of the errors in the
population (Fama, 1965; Wooldridge, 2009). Keeping in mind that the exact inference
based on t and F statistics requires the normality of the errors (Wooldridge, 2009; Gujarati
& Porter, 2009), these statistics are assumed to have large sample justifications without the
normality assumptions. Assuming normality of the estimated residuals from non-normally
distributed returns is apparently invalid. Other distributions have been suggested for
market returns (See, e.g.: (Cont, 2001)). However, due to the availability of statistical
software at hand, the Central Limit theorem is assumed to prevail and the distribution of
the samples in this study converges to normality with increasing sample size. In other
~ 12 ~
words, we assume that multivariate normal distribution is applicable for the markets
investigated here.
V.3. SIMPLE CORRELATION
Simple correlation coefficient indicates linear dependence between returns of
market j and those of USA market. The coefficient and their corresponding p-values from
significance tests are calculated using SPSS and summarized by regional classification in the
following table:
ρ SIG. ρ SIG. ρ SIG.
EGYPT 0.226 0.000 0.172 0.000 0.483 0.031
ISRAEL 0.507 0.000 0.552 0.000 0.515 0.000
SOUTH AFRICA 0.661 0.000 0.614 0.000 0.702 0.000
ARGENTINA 0.695 0.000 0.689 0.000 0.708 0.000
BRAZIL 0.797 0.000 0.785 0.000 0.825 0.000
CANADA 0.828 0.000 0.761 0.000 0.868 0.000
CHILE 0.704 0.000 0.688 0.000 0.733 0.000
MEXICO 0.821 0.000 0.794 0.000 0.843 0.000
AUSTRALIA 0.569 0.000 0.450 0.000 0.652 0.000
CHINA 0.095 0.015 0.066 0.118 0.171 0.092
HONGKONG 0.541 0.000 0.432 0.000 0.625 0.000
INDONESIA 0.323 0.000 0.346 0.000 0.305 0.002
INDIA 0.458 0.000 0.355 0.000 0.596 0.000
JAPAN 0.426 0.000 0.277 0.000 0.529 0.000
MALAYSIA 0.334 0.000 0.298 0.000 0.439 0.000
NEW ZEALAND 0.470 0.000 0.364 0.000 0.540 0.000
AMERICA
ASIA
FULL PERIOD TRANQUIL TURMOIL
AFRICA
~ 13 ~
ρ SIG. ρ SIG. ρ SIG.
PHILIPPINES 0.386 0.000 0.381 0.000 0.417 0.000
SINGAPORE 0.531 0.000 0.457 0.000 0.599 0.000
SOUTH KOREA 0.502 0.000 0.378 0.000 0.554 0.000
TAIWAN 0.402 0.000 0.327 0.000 0.499 0.000
THAILAND 0.372 0.000 0.268 0.000 0.503 0.000
EURO AREA 0.787 0.000 0.740 0.000 0.811 0.000
AUSTRIA 0.669 0.000 0.618 0.000 0.696 0.000
DENMARK 0.700 0.000 0.615 0.000 0.751 0.000
FRANCE 0.779 0.000 0.753 0.000 0.793 0.000
GERMANY 0.788 0.000 0.711 0.000 0.828 0.000
NETHERLANDS 0.606 0.000 0.606 0.000 0.605 0.000
RUSSIA 0.455 0.000 0.498 0.000 0.425 0.000
SPAIN 0.734 0.000 0.674 0.000 0.765 0.000
SWEDEN 0.717 0.000 0.672 0.000 0.743 0.000
SWITZERLAND 0.728 0.000 0.687 0.000 0.752 0.000
UNITED KINGDOM 0.767 0.000 0.737 0.000 0.782 0.000
FULL PERIOD TRANQUIL TURMOIL
EUROPE
ASIA
Table 7. Simple Correlation Coefficients of with USA Market – Regional Classification
The simple correlation coefficients show that the linear dependence between
international equity markets and the USA market has a somewhat regular pattern when
grouped by regional classification. Markets in Africa region show low correlations to USA,
most notably for Egypt. Surprisingly, however, South Africa has a rather high correlation to
the USA. Markets in America, both emerging (Argentina, Brazil, Chile, and Mexico) and
developed (Canada), have high correlation to the USA market. The same can be said for
European countries, aside from one emerging market in this region, namely Russia.
Compared to other Western European countries, two markets, i.e. Austria and the
Netherlands have relatively lower correlation to USA. Emerging and developed markets in
Asia exhibit relatively lower correlations to the USA market, most notably Japan which is a
developed economy and the second largest equity market worldwide (Elton, Gruber,
Brown, & Goetzmann, 2011).
~ 14 ~
The estimated coefficients showing non-significant linear dependence to USA are
marked in bold and italic numbers. It is found China has no significant correlation to the
United States during the tranquil and turmoil sub-samples. Even though its correlation to
the United States for the full sample period is significant, albeit very low, China will be
excluded from further analysis. For the rest of the countries considered in this study, all of
the correlation coefficients are statistically significant for α = 5%.
The results suggest that regional proximity play a role on cross-border
interdependence. These findings are in line with those from previous study (Bekaert &
Hodrick, 2009). Re-grouping the countries based on their income-level, the correlations
coefficients are presented as:
~ 15 ~
ρ SIG. ρ SIG. ρ SIG.
EGYPT 0.226 0.000 0.172 0.000 0.483 0.031
INDONESIA 0.323 0.000 0.346 0.000 0.305 0.002
INDIA 0.458 0.000 0.355 0.000 0.596 0.000
PHILIPPINES 0.386 0.000 0.381 0.000 0.417 0.000
THAILAND 0.372 0.000 0.268 0.000 0.503 0.000
ARGENTINA 0.695 0.000 0.689 0.000 0.708 0.000
BRAZIL 0.797 0.000 0.785 0.000 0.825 0.000
CHILE 0.704 0.000 0.688 0.000 0.733 0.000
MALAYSIA 0.334 0.000 0.298 0.000 0.439 0.000
MEXICO 0.821 0.000 0.794 0.000 0.843 0.000
RUSSIA 0.455 0.000 0.498 0.000 0.425 0.000
SOUTH AFRICA 0.661 0.000 0.614 0.000 0.702 0.000
AUSTRALIA 0.569 0.000 0.450 0.000 0.652 0.000
AUSTRIA 0.669 0.000 0.618 0.000 0.696 0.000
CANADA 0.828 0.000 0.761 0.000 0.868 0.000
DENMARK 0.700 0.000 0.615 0.000 0.751 0.000
EURO AREA 0.787 0.000 0.740 0.000 0.811 0.000
FRANCE 0.779 0.000 0.753 0.000 0.793 0.000
GERMANY 0.788 0.000 0.711 0.000 0.828 0.000
HONGKONG 0.541 0.000 0.432 0.000 0.625 0.000
ISRAEL 0.507 0.000 0.552 0.000 0.515 0.000
JAPAN 0.426 0.000 0.277 0.000 0.529 0.000
NETHERLANDS 0.606 0.000 0.606 0.000 0.605 0.000
NEW ZEALAND 0.470 0.000 0.364 0.000 0.540 0.000
SINGAPORE 0.531 0.000 0.457 0.000 0.599 0.000
SOUTH KOREA 0.502 0.000 0.378 0.000 0.554 0.000
SPAIN 0.734 0.000 0.674 0.000 0.765 0.000
SWEDEN 0.717 0.000 0.672 0.000 0.743 0.000
SWITZERLAND 0.728 0.000 0.687 0.000 0.752 0.000
UNITED KINGDOM 0.767 0.000 0.737 0.000 0.782 0.000
LOWER-MIDDLE INCOME
UPPER-MIDDLE INCOME
HIGH INCOME
FULL PERIOD TRANQUIL TURMOIL
Table 8. Simple Correlation Coefficients with USA Market – Income-Level Classification
From the table above, it can be seen that all of the lower-middle income countries
have low correlation to the USA market. The countries in the upper-middle income group
have high correlation to the United States, except Malaysia and Russia. Most of the
countries in high income group show relatively higher correlation to the USA market
compared to other income groups. The lowest correlation exhibits by a country in this
income level, i.e. possess macroeconomic similarities to the United States, is that
calculated from Japan market
~ 16 ~
As for the coefficients estimated for the two sub-samples, most of these
correlation coefficients show an increase in the crisis sub-sample compared to those in the
tranquil and full periods. This feature of increasing correlations during the crisis-period has
been well documented in previous studies (See, for instance, (King, Sentana, & Wadhwani,
1994; Ramchand & Susmel, 1998; Morana & Beltratti, 2008; Bekaert & Hodrick, 2009). Two
markets show relatively stable correlation coefficients for the three periods, i.e. Israel and
the Netherlands. Two exceptional markets in this study are Russia and Indonesia stock
markets. Their correlations with United States market are lower during the crisis sub-
sample compared to those from either full or tranquil period.
In Russia case, lower correlation coefficient is probably due to the time window
definition for crisis period in this study. The free-fall of stock markets in Russia was
noticeable around mid September and trading in this country was suspended on 17
September 2008 (Bush, 2008). By re-defining the tranquil period from the beginning of data
collection to 31/08/2008 and the crisis period from 01/09/2008 – 31/03/2009, Russia’s
correlations with the USA are 0.401 and 0.466 for the re-defined tranquil and crisis period,
respectively. The result for Indonesian market is an interesting phenomenon, considering
that in October 2008 the trading in Indonesian stock market Jakarta Stock Exchange was
suspended due massive sell-outs (SPIEGEL Staff, 2008). Nevertheless, the heterogeneity of
the direction of cross-market correlation during a high volatility period has been reported
in previous study (Corsetti, Pericoli, & Sbracia, 2001).
~ 17 ~
V.4. SERIAL- AND CROSS-CORRELATION TEST
In order to justify the application of multivariate financial time series, such as
Vector Autoregressive (VAR) model employed in this study, serial- and cross-correlations
between the returns of market j and those of USA are investigated. For covariate m = 2 and
lag order p = 3 the multivariate statistics ( ) are summarized in the table below:
COUNTRY Q2(3) COUNTRY Q2(3) COUNTRY Q2(3)
EGYPT 206.35 AUSTRALIA 604.74 EURO AREA 431.94
ISRAEL 173.80 HONG KONG 373.15 AUSTRIA 450.22
SOUTH AFRICA 407.17 INDONESIA 318.76 DENMARK 417.75
INDIA 261.26 FRANCE 461.73
ARGENTINA 341.92 JAPAN 446.81 GERMANY 356.93
BRAZIL 323.93 MALAYSIA 368.77 NETHERLANDS 646.18
CANADA 325.19 NEW ZEALAND 520.00 RUSSIA 311.73
CHILE 325.09 PHILIPPINES 502.05 SPAIN 426.62
MEXICO 339.91 SINGAPORE 359.00 SWEDEN 402.64
SOUTH KOREA 338.65 SWITZERLAND 383.06
TAIWAN 391.77 UNITED KINGDOM 498.74
THAILAND 306.82
ASIA
AMERICA
EUROPEAFRICA
Table 9. Multivariate Ljung-Box Statistics
The critical value of distribution for α = 5% and degrees of freedom
is 21.026 (Berenson, Levine, & Krehbiel, 2009). Therefore, it can be concluded that all the
returns data in this study have significant serial- and cross-correlations with its past values
and the past values of USA market. Thus, the application of VAR model with p = 3 is
justified to remove these linear dependencies. Since the lag order is found not to change
the conclusion of the conditional correlation analysis (Forbes & Rigobon, 2002), it is not
deemed necessary to perform joint test for longer lag.
V.5. REGRESSION ANALYSIS
For a specified VAR model, the parameters can be estimated using either the
ordinary least squares method (OLS) or the maximum likelihood estimation (Tsay, 2005).
Since the two methods are asymptotically equivalent, the OLS method is chosen for this
~ 18 ~
study due to the availability of statistical software. The returns data are regressed for three
different periods: full, tranquil and turmoil periods. Since the lag order p = 3, the regression
is performed from the observation at time t = p + 1 = 4. It is also observed that the power
of the regression model increase for the crisis sub-sample, suggesting that market returns
at this period are more linearly dependent with each other. For a complete list of the OLS
estimated parameters and their corresponding t-tests, please refer to the Appendix.
Meanwhile the results of the F test and coefficient of determination of the regressions
are produced using SPSS and summarized in the following table:
F-TEST SIG R2 F-TEST SIG R2 F-TEST SIG R2
CMA 24.23 0.00 0.38 25.32 0.00 0.40 6.24 0.01 0.91
NYSE 4.41 0.00 0.10 8.43 0.00 0.18 3.64 0.05 0.86
TEL100 15.93 0.00 0.27 23.85 0.00 0.37 1.02 0.46 0.36
NYSE 10.19 0.00 0.19 9.71 0.00 0.19 2.33 0.04 0.56
JSE 51.91 0.00 0.49 33.51 0.00 0.42 11.91 0.00 0.61
NYSE 18.22 0.00 0.25 17.65 0.00 0.28 3.80 0.00 0.33
F-TEST SIG R2 F-TEST SIG R2 F-TEST SIG R2
MERV. 34.76 0.00 0.40 25.45 0.00 0.36 6.33 0.00 0.50
NYSE 13.03 0.00 0.20 11.94 0.00 0.21 2.60 0.01 0.29
BOVES. 37.57 0.00 0.39 28.79 0.00 0.36 8.50 0.00 0.52
NYSE 19.83 0.00 0.25 18.53 0.00 0.27 3.57 0.00 0.31
TSX 34.88 0.00 0.38 27.36 0.00 0.36 5.42 0.00 0.43
NYSE 19.49 0.00 0.26 16.20 0.00 0.25 3.35 0.00 0.32
IPSA 42.79 0.00 0.44 27.51 0.00 0.38 10.77 0.00 0.60
NYSE 17.54 0.00 0.25 14.18 0.00 0.24 3.36 0.00 0.32
IPC 39.80 0.00 0.42 25.81 0.00 0.36 9.30 0.00 0.57
NYSE 18.32 0.00 0.25 14.59 0.00 0.24 3.40 0.00 0.32
F-TEST SIG R2 F-TEST SIG R2 F-TEST SIG R2
AOX 97.20 0.00 0.63 66.40 0.00 0.57 17.32 0.00 0.70
NYSE 22.10 0.00 0.28 18.53 0.00 0.27 4.26 0.00 0.36
HSI 38.76 0.00 0.42 33.23 0.00 0.43 8.31 0.00 0.54
NYSE 16.74 0.00 0.24 14.76 0.00 0.25 4.11 0.00 0.37
TRANQUIL TURMOIL
AUS
HKG
ASIA
EGY
AFRICA
AMERICA
FULL
TRANQUIL TURMOIL
FULL TRANQUIL TURMOIL
MEX
ISR
SAF
FULL
ARG
BRA
CAN
CHILE
~ 19 ~
F-TEST SIG R2 F-TEST SIG R2 F-TEST SIG R2
JKSE 33.89 0.00 0.40 29.04 0.00 0.39 5.07 0.00 0.46
NYSE 15.26 0.00 0.23 16.31 0.00 0.27 2.08 0.03 0.26
BSE30 25.94 0.00 0.34 28.81 0.00 0.39 4.06 0.00 0.42
NYSE 14.32 0.00 0.22 12.81 0.00 0.22 2.12 0.03 0.27
NIKKEI 61.08 0.00 0.54 31.17 0.00 0.41 14.79 0.00 0.71
NYSE 12.79 0.00 0.20 12.05 0.00 0.21 2.86 0.00 0.32
KLCI 39.40 0.00 0.43 44.36 0.00 0.50 4.86 0.00 0.45
NYSE 15.37 0.00 0.23 14.61 0.00 0.24 2.85 0.00 0.32
NZX50 73.41 0.00 0.57 52.84 0.00 0.53 14.22 0.00 0.66
NYSE 18.48 0.00 0.25 18.88 0.00 0.28 3.42 0.00 0.32
PSEI20 74.68 0.00 0.59 53.30 0.00 0.55 23.69 0.00 0.77
NYSE 21.86 0.00 0.29 16.74 0.00 0.27 4.57 0.00 0.39
STI 32.83 0.00 0.37 35.05 0.00 0.43 4.75 0.00 0.40
NYSE 18.32 0.00 0.25 17.54 0.00 0.27 3.77 0.00 0.35
KOSPI 39.67 0.00 0.43 28.19 0.00 0.39 7.13 0.00 0.50
NYSE 18.28 0.00 0.26 9.31 0.00 0.17 4.53 0.00 0.38
TWSE 42.19 0.00 0.44 34.93 0.00 0.44 8.65 0.00 0.56
NYSE 19.17 0.00 0.27 16.95 0.00 0.27 3.03 0.00 0.31
S.E.T 28.23 0.00 0.36 18.23 0.00 0.30 8.17 0.00 0.27
NYSE 14.49 0.00 0.22 11.97 0.00 0.22 3.23 0.00 0.32
F-TEST SIG R2 F-TEST SIG R2 F-TEST SIG R2
STOXX50 58.70 0.00 0.50 33.55 0.00 0.40 11.23 0.00 0.59
NYSE 20.19 0.00 0.26 18.02 0.00 0.27 4.13 0.00 0.35
ATX 56.70 0.00 0.51 31.65 0.00 0.41 11.94 0.00 0.62
NYSE 17.10 0.00 0.24 14.09 0.00 0.24 3.73 0.00 0.34
OMXC 65.42 0.00 0.54 37.37 0.00 0.44 13.09 0.00 0.63
NYSE 19.99 0.00 0.26 17.84 0.00 0.27 3.88 0.00 0.34
CAC40 61.44 0.00 0.51 34.17 0.00 0.41 12.09 0.00 0.61
NYSE 20.20 0.00 0.26 18.13 0.00 0.27 4.12 0.00 0.35
DAX30 48.94 0.00 0.46 32.50 0.00 0.40 8.23 0.00 0.52
NYSE 20.94 0.00 0.26 18.46 0.00 0.27 4.13 0.00 0.35
AEX 34.70 0.00 0.37 18.30 0.00 0.27 9.26 0.00 0.55
NYSE 87.08 0.00 0.60 56.61 0.00 0.53 17.37 0.00 0.69
RTSI 33.51 0.00 0.39 31.37 0.00 0.41 5.75 0.00 0.47
NYSE 18.42 0.00 0.26 15.46 0.00 0.26 3.58 0.00 0.36
MSE 59.94 0.00 0.51 31.69 0.00 0.39 11.80 0.00 0.61
NYSE 20.46 0.00 0.26 17.34 0.00 0.26 4.12 0.00 0.35
OMXS 56.40 0.00 0.50 35.67 0.00 0.43 10.17 0.00 0.58
NYSE 18.97 0.00 0.25 15.94 0.00 0.25 3.68 0.00 0.33
SSMI 57.40 0.00 0.50 28.08 0.00 0.37 14.39 0.00 0.65
NYSE 18.43 0.00 0.25 14.84 0.00 0.24 4.41 0.00 0.37
FTSE100 5.13 0.00 0.42 38.50 0.00 0.44 10.47 0.00 0.57
NYSE 7.01 0.00 0.50 19.14 0.00 0.28 3.78 0.00 0.33
SWE
SWI
UK
DEN
FRA
GER
NED
RUS
SPA
FULL TRANQUIL TURMOIL
EUR
EUROPE
AUT
PHI
SIG
S.KOR
TAI
THA
NZ
INA
IND
JAP
MAL
ASIAFULL TRANQUIL TURMOIL
Table 10. Regression F-test and
Given the absence of heteroscedasticity in the residuals, the p-values of the F-test
statistics here indicate that almost all of regressions perform in this study are significant
with at least one of the OLS estimate is significantly different from zero for α = 5%. A
~ 20 ~
regression for Israel market for the crisis sub-sample found to be insignificant, i.e. all of its
parameters are not significantly different from zero. Therefore we exclude Israel from
further analysis.
The of the regression signifies the explanatory power of the fitted model
(Berenson, Levine, & Krehbiel, 2009). From the regression s of the VAR(3) model in this
study it can be conjectured that in general, USA market is less dependent on serial- and
cross-correlation with market j as indicated by the lower for regression perform on USA
market returns. Exceptions are Thailand in crisis period, the Netherlands for all periods, and
United Kingdom for full period. When for USA market is found to be larger than those
for the market j, it indicates that the latter is less dependent of serial- and cross-correlation
with USA. Nevertheless, by looking at individual t-test of the regression parameter, it can
be concluded that, holding other explanatory variables constant, most of the equity
markets exhibits pronounced cross-correlation with past values of USA market, except for
Egypt.
In addition to lower for the regression of USA return, the exogeneity of this
market is evidence on the p-values of t-test for each of its estimated parameters for lagged
returns of market j. Almost all past values of market j have no significant impact on USA
return. Only in tranquil period regression on Hong Kong past values there appears to be
some feedback to USA. The results of regression suggest that USA market is less dependent
on the feedback from other markets. Therefore it can be concluded that the exogeneity
assumption of the USA market is a reasonable one. The granger causality of USA market,
especially on Asian markets, has been suggested by previous study (Atteberry & Swanson,
1997; Cha & Cheung., 1998; Cheung, Cheung, & Ng, 2007; Ding, 2010).
~ 21 ~
The t-test of the constant term show that almost all of the intercepts are not
significantly different from zero. The p-values also suggest that serial correlation of market
j appears to become less significant during crisis period. The same pattern is also observed
for USA market, its linear dependence on its past values appear to decline during turmoil
times. Exceptions to this are observed in countries in Europe region. Most countries in this
region show pronounced serial correlation in all periods. United Kingdom becomes more
serially correlated in crisis period. From all European countries, only Russia shows a
decrease in serial correlation during high volatility period. Taking the joint impact of all the
explanatory variables into consideration, the linear dependence between market j and USA
market appears to increase during the turmoil period as indicated by the increase in
values for this period.
Regarding past values of interest rates, the dependence of each of market returns
on their respective interest rates and of USA interest rates is less significant. However, it is
observed that there is a dependence of USA return is on daily short-term interest rates of
several markets, namely Japan and United Kingdom.
V.6. RESIDUALS ANALYSIS
In order to proceed with the correlation analysis, the regression residuals are
analysed to test whether assumptions underlying the OLS estimation are not violated.
Residuals analysis is also necessary to determine whether the fitted model selected is an
appropriate model. There are four assumptions of regression, namely: linearity,
independence of errors, normality of error and equal variance (Berenson, Levine, &
Krehbiel, 2009). As mentioned previously, the normality of the residuals is not analysed
because of large sample justification.
~ 22 ~
Linearity testing of residuals is a procedure to check whether there is a relationship
between the explanatory variables and the residuals. The residuals series are found to
be uncorrelated with the past value (p > 0) for all time series models (Tsay, 2005). Due
to the time constraint, any relationship between residuals and the past values of interest
rates will be assumed away. The robustness of this assumption will be tested in the
sensitivity analysis by removing the lagged values of interest rates from the right hand side
(RHS) variables and compare the resulting correlation to that of the original model which
include lagged interest rates as RHS variables.
Therefore we proceed with the Durbin-Watson (DW) test to check the serial
correlation of the residuals. The DW statistics are produced using SPSS and the results are
as follows:
AFRICA MKT. J MKT. USA MKT. J MKT. USA MKT. J MKT. USA
EGYPT 1.99 1.98 2.00 2.00 2.42 1.86
ISRAEL 1.96 2.00 1.93 1.98 2.01 2.11
SOUTH AFRICA 1.97 1.97 1.94 1.97 1.91 2.00
AMERICA MKT. J MKT. USA MKT. J MKT. USA MKT. J MKT. USA
ARGENTINA 1.94 1.99 1.97 1.97 1.87 2.03
BRAZIL 1.96 1.97 1.92 1.94 2.02 2.00
CANADA 1.89 1.94 1.87 1.93 1.88 1.93
CHILE 1.98 1.98 1.95 1.94 2.03 2.05
MEXICO 1.99 1.98 1.98 1.96 1.97 2.00
ASIA MKT. J MKT. USA MKT. J MKT. USA MKT. J MKT. USA
AUSTRALIA 1.99 1.96 1.96 1.94 1.96 1.95
HONG KONG 1.94 1.92 1.97 1.97 1.91 1.90
INDONESIA 2.02 2.02 1.99 1.89 2.00 2.10
INDIA 1.96 1.90 1.98 1.97 1.89 1.78
JAPAN 1.96 1.98 1.95 1.99 1.95 1.95
MALAYSIA 1.95 2.01 1.88 1.99 2.03 2.03
NEW ZEALAND 2.00 2.00 1.95 1.95 1.97 2.04
PHILIPPINES 1.91 1.96 1.91 2.00 1.83 1.92
SINGAPORE 2.00 2.00 1.97 1.97 1.99 2.07
SOUTH KOREA 1.99 1.94 1.99 1.94 1.99 1.93
TAIWAN 1.98 1.94 1.98 1.95 1.93 1.97
THAILAND 1.96 2.01 1.92 1.96 1.96 1.96
FULL TRANQUIL TURMOIL
~ 23 ~
EUROPE MKT. J MKT. USA MKT. J MKT. USA MKT. J MKT. USA
EURO AREA 1.87 1.91 1.89 1.94 1.75 1.90
AUSTRIA 1.93 1.98 1.93 1.96 1.81 1.97
DENMARK 1.84 1.94 1.91 1.95 1.68 1.95
FRANCE 1.85 1.91 1.88 1.94 1.72 1.91
GERMANY 1.89 1.93 1.92 1.95 1.83 1.93
NETHERLANDS 1.96 1.95 1.98 1.97 1.90 2.00
RUSSIA 2.01 1.96 1.92 1.91 2.06 2.00
SPAIN 1.87 1.93 1.91 1.98 1.72 1.72
SWEDEN 1.87 1.93 1.92 1.95 1.71 1.92
SWITZERLAND 1.87 1.95 1.90 1.96 1.74 1.99
UNITED KINGDOM 1.93 1.93 1.96 1.95 1.72 1.92
FULL TRANQUIL TURMOIL
Table 11. Durbin-Watson Statistics of Regression Residuals
From the DW-statistics of market returns for all periods considered, it can be seen
that all values of DW statistics are close to 2. Therefore, it can be safely concluded that the
residuals obtained from this regression model are not serially correlated (Berenson, Levine,
& Krehbiel, 2009).
The Levene tests are performed on both the Australia market and the USA market
for full period. The residuals from each market are divided into ten sub-groups. The median
is selected for the equal variance test because it is has been suggested that employing
median instead of mean for Levene test provides good robustness against many types of
non-normal data while simultaneously maintaining good test power (NIST/SEMATECH).
The test statistics are LW = 1.15 and 0.56 for Australia and USA market,
respectively. The critical value of distribution with degree of freedom 699 for numerator
and 9 for denominator at level of significance α = 5% is 2.71 (Berenson, Levine, & Krehbiel,
2009). Therefore we do not reject the null hypothesis of equal variance. This statistic is
produced using Excel due to the non-availability of other statistical software. With limited
time available at hand, the possibilities of violation to residuals homoscedasticity
assumption for other markets are assumed away.
~ 24 ~
V.7. CORRELATION ANALYSIS
V.7.1. CONDITIONAL CORRELATION COEFFICIENTS
By conditioning the returns matrix on the past values of market j and USA market
and the past values of interest rates from each market, the linear dependence between
market j and USA market for each period and their significance tests are summarized in the
following table:
TRANQUIL SIG. CRISIS SIG.
EGYPT 0.175 0.000 0.149 0.001 0.178 0.452
SOUTH AFRICA 0.620 0.000 0.548 0.000 0.707 0.000
ARGENTINA 0.709 0.000 0.709 0.000 0.728 0.000
BRAZIL 0.786 0.000 0.778 0.000 0.831 0.000
CANADA 0.827 0.000 0.761 0.000 0.880 0.000
CHILE 0.702 0.000 0.687 0.000 0.748 0.000
MEXICO 0.825 0.000 0.794 0.000 0.884 0.000
AUSTRALIA 0.516 0.000 0.364 0.000 0.655 0.000
HONGKONG 0.496 0.000 0.350 0.000 0.625 0.000
INDONESIA 0.274 0.000 0.305 0.000 0.273 0.012
INDIA 0.465 0.000 0.305 0.000 0.662 0.000
JAPAN 0.289 0.000 0.158 0.000 0.395 0.000
MALAYSIA 0.290 0.000 0.240 0.000 0.416 0.000
NEW ZEALAND 0.402 0.000 0.257 0.000 0.501 0.000
PHILIPPINES 0.250 0.000 0.278 0.000 0.281 0.005
SINGAPORE 0.476 0.000 0.367 0.000 0.549 0.000
SOUTH KOREA 0.422 0.000 0.279 0.000 0.477 0.000
TAIWAN 0.291 0.000 0.216 0.000 0.410 0.000
THAILAND 0.335 0.000 0.204 0.000 0.486 0.000
ASIA
FULL VAR SIG. SEPARATE VAR
AFRICA
AMERICA
~ 25 ~
TRANQUIL SIG. CRISIS SIG.
EURO AREA 0.764 0.000 0.721 0.000 0.797 0.000
AUSTRIA 0.653 0.000 0.609 0.000 0.673 0.000
DENMARK 0.665 0.000 0.589 0.000 0.741 0.000
FRANCE 0.755 0.000 0.733 0.000 0.774 0.000
GERMANY 0.751 0.000 0.688 0.000 0.792 0.000
NETHERLANDS 0.462 0.000 0.474 0.000 0.386 0.000
RUSSIA 0.414 0.000 0.461 0.000 0.377 0.000
SPAIN 0.710 0.000 0.659 0.000 0.760 0.000
SWEDEN 0.682 0.000 0.656 0.000 0.704 0.000
SWITZERLAND 0.688 0.000 0.666 0.000 0.706 0.000
UNITED KINGDOM 0.754 0.000 0.719 0.000 0.787 0.000
EUROPE
FULL VAR SIG. SEPARATE VAR
Table 12. Conditional Correlation Coefficients by Regional Classification
All of the conditional correlations in Table 13 are statistically significant, except for
the correlation coefficient between Egypt and USA during the crisis period (marked in bold
and italic number). Therefore, Egypt will be excluded from further analysis.
Given the past values of the common factors, the conditional correlations between
market j and USA market show the same tendency as that of the simple coefficients.
Markets in America and Europe regions show high correlations with USA market, except for
the Netherlands and Russia. Both emerging and developed markets in Asia region show
relatively lower conditional correlation to the market in the United States. The results for
Africa region show a fragmented view. A less developed market such as Egypt show a very
low correlation to USA, with its coefficient during the high volatility period is not
statistically different from zero. On the other hand, a more developed market like South
Africa shows high correlation to USA.
By removing any serial- and cross-correlation in the market returns, the calculated
conditional correlation coefficients are in general lower than the simple coefficients in
Table 8 except for several countries. Those that are found to exhibit higher conditional
~ 26 ~
correlations are countries in America region. For countries in this region, the calculation
results show that the conditional correlation is relatively the same or higher than the
simple coefficient.
Grouping the countries based on their income-level, the conditional correlation
coefficients can be presented as:
TRANQUIL SIG. CRISIS SIG.
EGYPT 0.175 0.000 0.149 0.001 0.178 0.452
INDONESIA 0.274 0.000 0.305 0.000 0.273 0.012
INDIA 0.465 0.000 0.305 0.000 0.662 0.000
PHILIPPINES 0.250 0.000 0.278 0.000 0.281 0.005
THAILAND 0.335 0.000 0.204 0.000 0.486 0.000
ARGENTINA 0.709 0.000 0.709 0.000 0.728 0.000
BRAZIL 0.786 0.000 0.778 0.000 0.831 0.000
CHILE 0.702 0.000 0.687 0.000 0.748 0.000
MALAYSIA 0.290 0.000 0.240 0.000 0.416 0.000
MEXICO 0.825 0.000 0.794 0.000 0.884 0.000
RUSSIA 0.414 0.000 0.461 0.000 0.377 0.000
SOUTH AFRICA 0.620 0.000 0.548 0.000 0.707 0.000
AUSTRALIA 0.516 0.000 0.364 0.000 0.655 0.000
AUSTRIA 0.653 0.000 0.609 0.000 0.673 0.000
CANADA 0.827 0.000 0.761 0.000 0.880 0.000
DENMARK 0.665 0.000 0.589 0.000 0.741 0.000
EURO AREA 0.764 0.000 0.721 0.000 0.797 0.000
FRANCE 0.755 0.000 0.733 0.000 0.774 0.000
GERMANY 0.751 0.000 0.688 0.000 0.792 0.000
HONGKONG 0.496 0.000 0.350 0.000 0.625 0.000
JAPAN 0.289 0.000 0.158 0.000 0.395 0.000
HIGH INCOME
FULL VAR SIG. SEPARATE VAR
LOWER-MIDDLE INCOME
UPPER-MIDDLE INCOME
~ 27 ~
TRANQUIL SIG. CRISIS SIG.
NETHERLANDS 0.462 0.000 0.474 0.000 0.386 0.000
NEW ZEALAND 0.402 0.000 0.257 0.000 0.501 0.000
SINGAPORE 0.476 0.000 0.367 0.000 0.549 0.000
SOUTH KOREA 0.422 0.000 0.279 0.000 0.477 0.000
SPAIN 0.710 0.000 0.659 0.000 0.760 0.000
SWEDEN 0.682 0.000 0.656 0.000 0.704 0.000
SWITZERLAND 0.688 0.000 0.666 0.000 0.706 0.000
UNITED KINGDOM 0.754 0.000 0.719 0.000 0.787 0.000
FULL VAR SIG. SEPARATE VAR
HIGH INCOME
Table 13. Conditional Correlation Coefficients by Income Level Classification
The same conclusion can be discerned as that obtained from the calculation of
simple correlation coefficient. All of the lower-middle income countries have low
conditional correlation to the USA market. The countries in the upper-middle income group
have high correlation to the United States, except Malaysia and Russia. Most of the high
income countries show relatively high correlation to the USA market, notably those in the
Europe region. High income countries with relatively lower correlations are those in Asia
region and the Netherlands. Japan shows the lowest correlation for this group of income-
level.
On the other hand, almost all conditional correlations are higher during the crisis
period compared to those in the full and tranquil period, save for Indonesia, the
Netherlands and Russia. However, as stated by Forbes and Rigobon (2001; 2002), this
relatively higher correlation during the crisis period does not translate into contagion if the
increase between the turmoil times relative to the low volatility period is not statistically
significant. Following their methodology, conditional correlation coefficient for the crisis
period is estimated from the full period OLS residuals for each economy. These coefficients
for full and crisis periods are then adjusted for heteroscedasticity effect by taking into
account the relative increase of variance of returns in the crisis country.
~ 28 ~
The relative increase of variance is calculated between the two different periods:
turmoil and relatively low volatility periods. Following Forbes and Rigobon method, it is
calculated between crisis and full sample period. The USA market variance during crisis is
around 3.5 times higher compared to that in a more tranquil period.
It is worth noting that the correlation coefficients estimated from separate VAR(3)
model for the tranquil and turmoil sub-samples (tabulated in the third and fifth column on
Table 13-14) will not be adjusted for heteroscedasticity. These conditional correlation
coefficients will be employed for the second set of hypothesis testing. The summary of the
conditional coefficients from separate VAR, and the heteroscedasticity-adjusted correlation
coefficients are presented in the following table:
FULL CRISIS TRANQUIL CRISIS REL VAR FULL CRISIS
SOUTH AFRICA 0.620 0.706 0.548 0.707 3.32 0.36 0.43
ARGENTINA 0.709 0.725 0.709 0.728 3.63 0.42 0.44
BRAZIL 0.786 0.824 0.778 0.831 3.51 0.51 0.57
CANADA 0.827 0.876 0.761 0.880 3.37 0.58 0.66
CHILE 0.702 0.755 0.687 0.748 3.48 0.42 0.48
MEXICO 0.825 0.863 0.794 0.884 3.56 0.56 0.62
AUSTRALIA 0.516 0.654 0.364 0.655 3.51 0.27 0.38
HONGKONG 0.496 0.601 0.350 0.625 3.49 0.26 0.33
INDONESIA 0.274 0.267 0.305 0.273 3.51 0.13 0.13
INDIA 0.465 0.650 0.305 0.662 3.91 0.23 0.36
JAPAN 0.289 0.430 0.158 0.395 3.09 0.15 0.23
MALAYSIA 0.290 0.399 0.240 0.416 3.79 0.14 0.20
NEW ZEALAND 0.402 0.513 0.257 0.501 3.40 0.20 0.27
AMERICA
ASIA
CONDITIONAL CORRELATIONSADJ. CORRELATIONS
FULL VAR SEPARATE VAR
AFRICA
~ 29 ~
FULL CRISIS TRANQUIL CRISIS REL VAR FULL CRISIS
PHILIPPINES 0.250 0.283 0.278 0.281 3.19 0.13 0.14
SINGAPORE 0.476 0.571 0.367 0.549 3.51 0.25 0.31
SOUTH KOREA 0.422 0.490 0.279 0.477 3.35 0.22 0.26
TAIWAN 0.291 0.403 0.216 0.410 3.54 0.14 0.20
THAILAND 0.335 0.513 0.204 0.486 3.40 0.17 0.27
EURO AREA 0.764 0.797 0.721 0.797 3.47 0.49 0.53
AUSTRIA 0.653 0.689 0.609 0.673 3.46 0.38 0.41
DENMARK 0.665 0.734 0.589 0.741 3.43 0.39 0.46
FRANCE 0.755 0.777 0.733 0.774 3.46 0.48 0.51
GERMANY 0.751 0.790 0.688 0.792 3.52 0.47 0.52
NETHERLANDS 0.462 0.419 0.474 0.386 3.48 0.24 0.21
RUSSIA 0.414 0.385 0.461 0.377 3.48 0.21 0.19
SPAIN 0.710 0.756 0.659 0.760 3.50 0.43 0.48
SWEDEN 0.682 0.706 0.656 0.704 3.49 0.40 0.43
SWITZERLAND 0.688 0.722 0.666 0.706 3.42 0.41 0.44
UNITED KINGDOM 0.754 0.783 0.719 0.787 3.43 0.48 0.51
EUROPE
ASIA
CONDITIONAL CORRELATIONSADJ. CORRELATIONS
FULL VAR SEPARATE VAR
Table 14. Conditional and Unconditional Correlation Coefficients
V.7.2. HYPOTHESES TESTING
The test statistics calculated and reported here are the Fisher transformation ( )
because, as mentioned in the previous chapter, its distribution is closer to normal
distribution (Bradley & Taqqu, 2005). Each of hypothesis testing is performed with the null
hypothesis of equal correlation, i.e. no contagion, as defined according to the Equation 54
and Equation 58. The statistics for each of the hypothesis testing are denoted as for
the comparison between the heteroscedasticity-adjusted coefficients and for the
comparison between the conditional correlations of the tranquil and turmoil periods. These
are one-tailed tests with critical value = 1.65 for α = 5%. The results of the tests statistics
and testing decisions are summarized as follows:
~ 30 ~
FULL TRA CRI SE FR2,1 CONT. SE FR2,2 CONT.
SOUTH AFRICA 672 568 104 0.11 0.86 NO 0.11 2.46 YES
ARGENTINA 644 554 90 0.11 0.17 NO 0.12 0.34 NO
BRAZIL 730 623 107 0.10 0.70 NO 0.11 1.43 NO
CANADA 695 595 100 0.11 1.19 NO 0.11 3.44 YES
CHILE 659 559 100 0.11 0.65 NO 0.11 1.15 NO
MEXICO 666 568 98 0.11 0.84 NO 0.11 2.81 YES
AUSTRALIA 709 605 104 0.11 1.09 NO 0.11 3.74 YES
HONGKONG 648 551 97 0.11 0.74 NO 0.11 3.29 YES
INDONESIA 631 547 84 0.12 0.03- NO 0.12 0.29- NO
INDIA 629 548 81 0.12 1.19 NO 0.12 3.98 YES
JAPAN 629 543 86 0.12 0.72 NO 0.12 2.19 YES
MALAYSIA 643 558 85 0.12 0.51 NO 0.12 1.67 YES
NEW ZEALAND 685 585 100 0.11 0.68 NO 0.11 2.62 YES
PHILIPPINES 646 546 100 0.11 0.17 NO 0.11 0.03 NO
SINGAPORE 675 578 97 0.11 0.63 NO 0.11 2.09 YES
SOUTH KOREA 641 541 100 0.11 0.41 NO 0.11 2.11 YES
TAIWAN 647 552 95 0.11 0.56 NO 0.11 1.92 YES
THAILAND 621 526 95 0.11 1.01 NO 0.11 2.87 YES
EURO AREA 714 608 106 0.11 0.52 NO 0.11 1.69 YES
AUSTRIA 659 560 99 0.11 0.35 NO 0.11 0.99 NO
DENMARK 690 586 104 0.11 0.77 NO 0.11 2.57 YES
FRANCE 715 609 106 0.11 0.33 NO 0.11 0.89 NO
GERMANY 711 607 104 0.11 0.58 NO 0.11 2.16 YES
NETHERLANDS 712 607 105 0.11 0.26- NO 0.11 1.01- NO
RUSSIA 644 553 91 0.11 0.15- NO 0.11 0.89- NO
SPAIN 708 604 104 0.11 0.58 NO 0.11 1.91 YES
SWEDEN 686 584 102 0.11 0.25 NO 0.11 0.82 NO
SWITZERLAND 690 586 104 0.11 0.39 NO 0.11 0.70 NO
UNITED KINGDOM 708 602 106 0.11 0.44 NO 0.11 1.48 NO
EUROPE
SAMPLE SIZE FISHER TRANS.1 FISHER TRANS.2
AFRICA
AMERICA
ASIA
Table 15. Fisher Transformation Statistics by Regional Classification
The results of the first hypothesis testing are in agreement with those found by
Forbes and Rigobon. Virtually there was no shift-contagion found in the stock market crash
of 2008. The test statistics calculated for the unconditional correlation for all countries
suggested that widespread shift-contagion did not occur during the stock market crash of
2008 and there was only a continuance of, albeit high, comovement between the United
~ 31 ~
States and other markets. The results from the first hypothesis testing appear to support
the non-crisis-contingent theory, i.e. there is no change in the propagation mechanisms.
However, the tests performed using conditional correlation coefficients from
separate VARs present different results. As suggested by Dungey and Zhumabekova (2001),
a more powerful test is to perform separate estimation of the VAR model for tranquil and
turmoil periods and compare the resulting conditional correlation coefficients between the
two periods. Following this procedure, it is found that several countries experienced shift-
contagion during the period investigated in this study. In other words, there was a
significant increase of correlation coefficient observed in the crisis period compared to that
in a relatively low volatility period.
In Africa region, South Africa is found to be highly correlated with USA market.
During the crisis period defined in this study, there is evidence of shift-contagion in this
market. In America region, only Canada and Mexico are found to exhibit shift-contagion
during the turmoil period. There is evidence of significant increase in market linkages
between USA and each of the market in Asia region, whether developed (e.g. Japan) or
emerging ones, except for Indonesia and the Philippines. On the other hand, most of the
markets in Europe did not experience shift-contagion except for the aggregate market of
Euro Area, Denmark, Germany, and Spain.
Relying on the second hypothesis testing and grouping the countries into their
income-level, the data presents a clearer pattern:
~ 32 ~
FR2,1 CONTAGION FR2,2 CONTAGION
INDONESIA 0.03- NO 0.29- NO
INDIA 1.19 NO 3.98 YES
PHILIPPINES 0.17 NO 0.03 NO
THAILAND 1.01 NO 2.87 YES
ARGENTINA 0.17 NO 0.34 NO
BRAZIL 0.70 NO 1.43 NO
CHILE 0.65 NO 1.15 NO
MALAYSIA 0.51 NO 1.67 YES
MEXICO 0.84 NO 2.81 YES
RUSSIA 0.15- NO 0.89- NO
SOUTH AFRICA 0.86 NO 2.46 YES
AUSTRALIA 1.09 NO 3.74 YES
AUSTRIA 0.35 NO 0.99 NO
CANADA 1.19 NO 3.44 YES
DENMARK 0.77 NO 2.57 YES
EURO AREA 0.52 NO 1.69 YES
FRANCE 0.33 NO 0.89 NO
GERMANY 0.58 NO 2.16 YES
HONGKONG 0.74 NO 3.29 YES
JAPAN 0.72 NO 2.19 YES
NETHERLANDS 0.26- NO 1.01- NO
NEW ZEALAND 0.68 NO 2.62 YES
SINGAPORE 0.63 NO 2.09 YES
SOUTH KOREA 0.41 NO 2.11 YES
SPAIN 0.58 NO 1.91 YES
SWEDEN 0.25 NO 0.82 NO
SWITZERLAND 0.39 NO 0.70 NO
UNITED KINGDOM 0.44 NO 1.48 NO
FISHER TRANS.1 FISHER TRANS.2
LOWER-MIDDLE INCOME
UPPER-MIDDLE INCOME
HIGH INCOME
Table 16. Fisher Transformation Statistics by Income-Level Classification
From the second hypothesis testing presented in the table above it can be seen
that most of the shift-contagion in the stock market crisis of 2008 appears to exist
predominantly in the high-income countries, i.e. countries with macroeconomic similarities
to the crisis country. Another way to look at it is that the countries with evidence of shift-
contagion are developed markets which are more integrated to global financial market
~ 33 ~
where the United States is the most dominant player. Therefore, they are more at risk to
shock propagated from USA.
Looking at the correlation coefficients between market j and USA, there appear to
be a relationship between high market interdependence and their regional proximity.
However, the results from correlation test do not suggest a pronounced linkage between
regional proximity to the crisis country and shift-contagion. Relying on the results
calculated from the conditional correlation coefficient, shift-contagion appears to be more
pronounced in the Asia region, most notably those with high income level.
V.8. SENSITIVITY ANALYSIS
Due to the time constraint, sensitivity analysis is performed as a multivariate
analysis between the New York Stock Exchange in the United States and the MERVAL in
Argentina. Several regressions are performed for different variables in the model:
increasing lag order to 5, decreasing lag order to 1, changing the market return of
Argentina into those calculated from index denoted in local currency, changing the lagged
values of daily short-term interest rates into past values of MSCI World Index, excluding the
lagged interest rates, and redefining the time window. The conditional and adjusted
correlation coefficients calculated from the residuals of regression performed with the
specified variables are summarized in the following table:
FULL CRISIS TRA CRISIS δ FULL CRISIS FULL TRA CRI
LAG-3 0.709 0.725 0.709 0.728 3.63 0.423 0.439 644 554 90
LAG-5 0.710 0.734 0.699 0.741 3.62 0.425 0.449 642 552 90
LAG1 0.706 0.730 0.697 0.717 3.64 0.420 0.444 646 556 90
LOCAL CURRENCY 0.709 0.725 0.713 0.731 3.65 0.423 0.439 641 551 90
WORLD INDEX 0.708 0.732 0.701 0.735 3.62 0.423 0.447 636 546 90
ONLY LAGGED RET 0.708 0.727 0.702 0.727 3.63 0.422 0.441 644 554 90
TIME WINDOW 2 0.726 0.732 0.720 0.736 1.96 0.523 0.530 184 138 46
TIME WINDOW 3 0.726 0.768 0.535 0.773 1.43 0.560 0.609 184 119 65
FULL OLS SEPARATE OLS UNCONDITIONAL CORR SAMPLE SIZE
Table 17. Correlation Coefficients of Sensitivity Analysis
~ 34 ~
The test statistics for the differences between correlation coefficient of the crisis
and of the relatively low volatility period are:
SE FR2,1 CONTAGION SE FR2,2 CONTAGION
LAG-3 0.11 0.17 NO 0.12 0.34 NO
LAG-5 0.11 0.26 NO 0.12 0.76 NO
LAG1 0.11 0.26 NO 0.12 0.35 NO
LOCAL CURRENCY 0.11 0.17 NO 0.12 0.32 NO
WORLD INDEX 0.11 0.26 NO 0.12 0.61 NO
ONLY LAGGED RET 0.11 0.20 NO 0.12 0.44 NO
TIME WINDOW 2 0.17 0.06 NO 0.18 0.19 NO
TIME WINDOW 3 0.15 0.51 NO 0.16 2.74 YES
FISHER TRANS. 2FISHER TRANS.1
Table 18. Fisher Transformation Statistics of Sensitivity Analysis
The results of the sensitivity analysis show that both hypothesis testing methods
are quite robust toward lag order. No different results obtained for different lag order, i.e.
no shift-contagion is found for Argentina stock market in the time period considered.
Changing the currency into local currency also does not affect the conclusion for this
market. Sensitivity analysis are also carried out by changing the common factor into past
values of a global index, in this study the global index chosen is MSCI World Index, and by
excluding aggregate shocks altogether. Changing the variables of the common factors does
not affect the results of the correlation rest. No shift-contagion is found in Argentina during
the stock market crash of 2008.
Some suggested that Forbes and Rigobon correlation analysis method consistently
over-rejects the hypothesis of contagion mostly due to the comparison of large sample of
non-crisis period to a small sample of crisis period (Dungey & Zhumabekova, 2001).
Therefore the analysis of time window sensitivity will be performed with different length of
crisis period. By shortening the length of both tranquil and turmoil period, i.e. changing
sample sizes, we come to the same conclusion as that obtained with longer period.
However, changing the specification of the turmoil period (in this study, moving it earlier to