across the countries involved.
3
We develop a theoretical model in which each time series of pairwise correlations may depend upon factors that characterize and influence the
extent of economic integration across the two markets in question. The set of all such pairwise equations is then estimated both as a pooled regression and as a system of
seemingly unrelated regressions that describes potential economic determinants of the correlation structure. This analysis is conducted on the subset of seven countries for which
complete economic data are available. Results indicate that the degree of international integration the magnitude of the correlations is positively associated with 1 world
market volatility and 2 a trend; while it is negatively related to 3 exchange rate volatility, 4 term structure differentials across markets, 5 real interest rate differentials,
and 6 the return on a world market index.
This analysis sheds light on the economic forces that influence the correlation structure over time, and thus the evolution in global capital market integration. For example, these
results corroborate a priori expectations that divergent macroeconomic behavior across countries tends to be associated with divergent behavior across national equity markets,
resulting in lower market correlations. In addition, the influence of economic factors 1 and 6 listed above indicate an increase in comovement across international equity
markets when world markets are more volatile andor falling. This outcome suggests a decline in the risk-reduction benefits of international diversification at the very time when
these benefits are needed most.
Finally, the economic model is employed to generate out-of-sample forecasts of the correlation structure. The forecast performance of this model dominates that of other
atheoretical models which ignore economic determinants of the correlation structure. This outcome adds credence to the validity of the theoretical economic model, and suggests that
modeling the correlation structure holds promise in assisting managers to exploit inter- national investment opportunities.
The paper proceeds as follows. Section II reviews the literature on stability in the correlation structure, discusses the data, and presents the stability tests. Section III
develops the theoretical model describing economic determinants of the correlation structure, and Section IV estimates the model. Section V compares the forecast perfor-
mance of this model with respect to alternative forecasting techniques. A final section summarizes and concludes.
II. Literature Review, Stock Market Data, and Stability Tests
Literature Review
The existing literature offers mixed evidence on the stability of the correlation structure. Several earlier studies by Panton et al. 1976, Watson 1980, and Philippatos et al.
1983 all find support for stable relationships across national equity markets. In contrast, Makridakis and Wheelwright 1974, Haney and Lloyd 1978, Maldonado and Saunders
1981, Fischer and Palasvirta 1990, Madura and Soenen 1992, Wahab and Lashgari 1993, and Longin and Solnik 1995 argue that the relationships are unstable. Falling
somewhere between these two camps, Kaplanis 1988 suggests that correlations are stable while covariances are unstable; Marcus et al. 1991 suggest that the holding period
3
For other studies that motivate this hypothesis, see Arshanapalli and Doukas 1993, Bachman et al. 1996, Bodurtha et al. 1989, Campbell and Hamao 1992, and Roll 1992.
Determinants of International Correlation
445
analyzed has a bearing on the correlation structure observed; and Meric and Meric 1989 find instability for shorter periods, offset by stability over longer periods.
The disparity in results across this literature is presumably attributable to the wide range of sample periods and sampling frequencies examined, as well as different meth-
odologies employed.
4
Interestingly, most recent studies tend to find greater instability, suggesting that interrelationships among national stock markets may have undergone a
substantive change during the 1980s.
Stock Market Data
The data include Morgan Stanley Capital International’s daily closing stock index values for ten national markets Australia, Canada, Germany, Hong Kong, Japan, Mexico,
Singapore, Switzerland, the United Kingdom, and the United States, as well as daily bilateral exchange rates between the US dollar and the nine other currencies, from 1972
through 1993.
5
The analysis is applied to daily returns for every national market, denominated both in US dollars and in the home currency.
Tests for Stability in the Correlation Matrix
From these time series of daily stock returns, we compute the correlation between every pair of national markets over each quarter during this 22-year sample period. The resulting
time series of 88 quarterly observations on the correlation matrix reveals the nature and extent of changes in the correlation structure over time. This quarterly time series is then
employed to test for stability in the correlation structure, using a Jennrich 1970 test for the equality of two correlation matrices.
6
Table 1 presents the results of three different approaches for investigating the hypoth- esis that the correlation matrix does not change over time. First, we examine the null
hypothesis that the correlation matrix does not change from one quarter to the next, across each of the 88 quarters in the sample period. Panel A of Table 1 presents the frequency
of rejections out of these 87 tests comparing consecutive quarterly correlation matrices. If the correlation matrix is truly constant, we would expect approximately nine rejections out
of 87 tests at the 0.10 level of significance along with five rejections at the 0.05 level and one
rejection at the 0.01 level. Panel A reveals that stability is rejected far more
4
Different studies in this literature employ data: 1 taken over different sample periods which sometimes extend prior to the early 1970s, when world equity and currency markets were more stable, and 2 taken at
different frequencies daily, weekly, monthly, quarterly, or annually.
5
Morgan Stanley Capital International MSCI data on individual firm stocks around the world represent approximately 60 of the world’s total market capitalization. From these data MSCI constructs national stock
indexes that are fully comparable. The ten national equity markets chosen for this analysis account for approximately 90 of the world’s total market capitalization.
6
Appendix A provides the formal Jennrich 1970 test. Data for Mexico are unavailable prior to 1988. Therefore, stability tests where both periods tested begin after 1988 use all ten countries. Otherwise only nine
countries are employed. Following Meric and Meric 1989, a Box M test is also applied to test for equality across correlation
matrices. The Jennrich 1970 test is the more conservative approach, designed specifically for testing equality of correlation matrices, while the Box M test is primarily used for investigating covariance matrices. In addition,
all stability tests have been performed using both Pearson and Spearman correlation estimates. Results are robust across both stability tests and both correlation measures, as well as across data using both US dollar returns and
home currency returns. For brevity, we report only results for the Jennrich test on Pearson correlations using US dollar-denominated data. All results are available upon request.
446
K. Bracker and P. D. Koch
Table 1.
Jennrich Tests for Equality of Two Correlation Matrices.
a
Pearson correlations are estimated from daily returns in U.S. dollars across ten national markets, for each quarter throughout the 22-year period, 1972–1993. The result is a time series that
embodies quarterly movements in the correlation matrix across national equity markets. The Jennrich 1970 test is applied to investigate the equality of:
A: consecutive quarterly correlation matrices; B: nonconsecutive quarterly correlation matrices one, two, and three quarters apart;
C: consecutive correlation matrices estimated over time intervals longer than one quarter. This Table presents the frequency of rejections in applying these Jennrich 1970 tests.
b
Panel A: Frequency of Rejections Across Consecutive Quarterly Correlation Matrices
Panel A 10 Level
1 2 p 5 .10 5 Level
1 2 p 5 .05 1 Level
1 2 p 5 .01 Number of times that equality is rejected out
of 87 Tests 39
29 13
Panel B: Frequency of Rejections Across Non-Consecutive Quarterly Correlation Matrices
Panel B: 10 Level
5 Level 1 Level
1 Quarter apart 86 tests 42
28 18
2 Quarters apart 85 tests 47
33 16
3 Quarters apart 84 tests 50
34 23
Panel C: Frequency of Rejections Across Consecutive Time Intervals Greater than One Quarter in Length
Panel C: 10 Level
5 Level 1 Level
Semiannual 43 tests 33
22 16
Annual 21 tests 20
19 16
Biannual 10 tests 10
10 9
Five-and-one-half years 3 tests 3
3 3
Eleven years 1 test 1
1 1
a
Jennrich 1970 provides a Chi-square statistic to test the equality of two correlation matrices; details appear in Appendix A.
b
Results are robust with respect to the use of Spearman correlations, home currency returns, and the alternative Box M test for equality across correlation matrices.
Indicates that the number of rejections is greater than expected by chance 1 of the time, within a binomial framework that bases the probability of acceptance for each individual test at p 5 .90, .95, and .99, and the probability of rejection at 1-p
5 .10, .05, and .01. Therefore, 1 2 p represents the significance level for each individual test. This binomial analysis is not applied to the last two rows in Panel C due to the small number of tests conducted in each case.
To elaborate, this binomial framework considers the outcome of each test to be drawn independently from a binomial distribution. If we consider an acceptance of the null in one trial to be a success, and a rejection to be a failure, then at the 10
level of significance the probability of success for every test is .90 and the probability of failure is .10. By viewing the sequence of tests this way, we can determine the ‘‘critical values’’ for the number of rejections expected at the 10, 5, and 1
significance levels. Given a probability of success at p 5 .90 the 10 level of significance, with 87 independent tests there is less than a 1 chance of rejecting the null more than 16 times. Similarly, given a probability of p 5 .95, there is less than
a 1 chance of rejecting the null more than 10 times. Finally, given a probability of success at p 5 .99, there is less than a 1 chance of rejecting the null more than 4 times. Since the numbers in each cell of Panel A are greater than these respective
‘‘critical values,’’ the number of rejections indicated in each cell of Panel A is greater than would be expected 1 of the time, under this binomial exercise.
Determinants of International Correlation
447
frequently than is expected by chance 39 rejections at the 0.10 level, 29 rejections at the 0.05 level, and 13 rejections at the 0.01 level.
We can more formally address the issue of whether the number of rejections docu- mented in Table 1 is “significantly greater than expected” at each level of significance,
by considering the outcome of every test as being drawn independently from a binomial distribution. If we consider an acceptance of the null in one trial to be a success, and a
rejection to be a failure, then at the 10 level of significance the probability of success for that trial is .90 and the probability of failure is .10. By viewing the sequence of tests
this way, we can determine the “critical values” for the number of rejections expected at the 10, 5, and 1 significance levels. Given a probability of success at p 5 .90 the
10 level of significance, with 87 independent tests there is less than a 1 chance of rejecting the null more than sixteen times. Similarly, given a probability of success at p 5
.95, there is less than a 1 chance of rejecting the null more than ten times. Finally, given a probability of success at p 5 .99, there is less than a 1 chance of rejecting the null more
than four times. Once again, because the numbers in Panel A of Table 1 are greater than these respective “critical values,” the number of rejections in each cell of Panel A is
greater than would be expected 1 of the time, under this binomial exercise.
Next, we consider the possibility that these quarterly correlation matrices may change more slowly over time, by investigating the equality of correlation matrices that are one,
two, and three quarters apart. Panel B of Table 1 presents the frequency of rejections across nonconsecutive quarterly correlation matrices, and once again reveals far more
rejections than could be expected by chance. Finally, Panel C considers the stability of the correlation matrix computed over longer time intervals of 6 months, 1 year, 2 years, 5
1
⁄
2
years, and 11 years. Results in Panel C uniformly indicate instability over these longer time periods as well.
While our results are consistent with most recent studies on this issue, these latter findings contrast with the results of Meric and Meric 1989, which suggest some
underlying long-run stability in the correlation matrix. This contrast is important. If there were truly long-run stability, then the short-run instability documented in Panels A and B
of Table 1 would not be critical for long-term investors. Instead, our results overwhelmingly indicate significant changes in the correlation matrix over both short and long time horizons.
These results provoke the question as to how and why the correlation structure varies over time. Before we proceed to address this question by developing the economic model,
we must investigate whether each time series of pairwise correlations contains a unit root. If changes in the correlation structure contain a unit root follow some form of random
walk, then our model of the correlation structure may result in identifying spurious relationships with economic variables Enders 1995.
In this light, we perform Augmented Dickey–Fuller ADF tests on each time series of quarterly pairwise correlations. Results are provided in Table 2 and indicate rejection of
the unit root hypothesis for 18 of the 21 time series of pairwise correlations, at the .10 level or better. Because the vast majority of these time series have no unit root, it is
reasonable to proceed with our attempt to model how and why the correlation structure changes over time.
III. Modeling Economic Determinants of Correlation Structure
