This paper investigates the time-varying bivariate co-movement between international stock market returns for a set of major equity indices. The selected indices represent the major stock markets of the G7 countries and the BRIC countries. This paper firstly paired the U.S. index with the remaining 10 equity indices in the sample, and then secondly, in a smaller setup, paired the U.K. index with the remaining European equity indices in the G7 (France, Germany and Italy).
To estimate and examine time-varying co-movement, this study used a combination of wavelet analysis and DCC-GARCH model. The inclusion of wavelet analysis, specifically maximum overlap discrete wavelet transform, allows for the comparison of how the co-movement varies over different timescales, while the DCC-GARCH modelling approach allows the co-movement to be tracked in time.
The time-varying estimates of conditional correlation are of special interest to investors when it comes to portfolio allocation and risk management. By investigating time-scale dependent co-movement the study takes into account that investors have different frequencies of investment activity, e.g., passive or active investment styles, and are interested in co-movement over different time horizons.
The broader results of this study support the presence of dynamic conditional correlations between the returns of the selected U.S. equity index and corresponding indices representing the stock markets of the remaining G7 countries and the BRIC countries. A similar conclusion was made when pairing the U.K. equity index with the corresponding indices of France, Germany and Italy.
The co-movement was weaker for the smaller timescales used in this study and thus the diversification benefits appeared to be concentrated over shorter investment horizons.
Regional belonging appeared to influence return co-movement to some extent. Canada exhibited the strongest return co-movement with the U.S. and the U.K. exhibited strong movement with France, Germany and Italy. Furthermore, the relatively weak co-movement observed between the U.S. and the BRIC markets, excluding Brazil, signals the existence of a developmental factor in stock market co-movement. Nevertheless, the BRIC countries do not appear to constitute a homogeneous group since Brazil deviates by displaying moderate co-movement with the U.S. at the smaller timescales.
The greatest diversification benefits were observed between the U.S. and the Asian countries used in this study. Japan displayed particularly weak correlation with the U.S.
over the examined time period as did China. India and Russia also displayed weak correlation but to lesser degrees than the two other markets.
Finally, the Brexit referendum results were observed to influence the co-movement between the U.K. and the other three European countries of the G7 at the smaller timescales. In the immediate post-referendum period these country pairs displayed a noticeable increase in their co-movement which lasted for several months. The same effect was not observed for the larger timescales.
7.1 Suggestions for further research
This study only considers co-movement between stock market returns and therefore one could expand the scope to also look at co-movement of returns of different asset classes.
Another potential extension of this study would be to explore a portfolio allocation strategy based on the timescale-dependent co-movement observations. Portfolios with different holding periods could be constructed according to low-correlation criteria. If one wants to compare or evaluate the performance of internationally diversified portfolios one might want to use a dataset involving more countries than used in this study.
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APPENDIX 1 DCC DESCRIPTIVE STATISTICS: U.S. AS A
APPENDIX 2 DCC DESCRIPTIVE STATISTICS: U.K. AS REFERENCE COUNTRY D1, D3 AND D6
d1 correlation
Mean Max Min SD
France
0.8110 0.9733 -0.2289 0.1299
Germany0.7875 0.9772 -0.2771 0.1372
Italy0.7238 0.9325 -0.1710 0.1464
d3 correlation
Mean Max Min SD
France
0.7822 0.9894 -0.6334 0.2389
Germany0.7562 0.9861 -0.6547 0.2570
Italy0.6957 0.9777 -0.6178 0.2839
d6 correlation
Mean Max Min SD
France