حرکت مشترک در بازارهای سهام بین المللی: یک دیدگاه بخشی

We investigate shifts in correlation patterns among international equity returns at the market level as well as the industry level. We develop a novel bivariate GARCH model for equity returns with a smoothly time-varying correlation and then derive a Lagrange Multiplier statistic to test the constant correlation hypothesis directly. Applying the test to weekly data from Germany, Japan, the UK and the US in the period 1980–2000, we find that correlations among the German, UK and US stock markets have doubled, whereas Japanese correlations have remained the same. Both dates of change and speeds of adjustment vary widely across countries and sectors.

Over the past twenty years, the importance of the domestic stock market in many industrialized economies has grown sharply, while at the same time the degree of comovement among international equity markets seems to have increased. As a result, national economies are more frequently affected by disturbances originating in foreign stock markets, and these disturbances also tend to have more far-reaching consequences. This is a widely held view among financial market participants, the media, academics and policy makers. It is argued that financial integration has been spurred by improved electronic communications, the worldwide liberalization of capital controls and financial innovation, as well as growing political and economic integration. However, it is unclear whether correlations among equity returns across countries really have increased. It is conceivable that this idea stems from a biased reading of the data. Discussions of stock market developments in the media may exaggerate the importance of infrequent, large, but simultaneously occurring changes in international stock returns. While such dramatic changes may seem to offer strong anecdotal evidence for greater comovement, a careful empirical investigation into this issue would need to take into account the behavior of returns during the entire sample period. An accurate assessment of the degree of comovement among international equity markets is important for several reasons. For investors, the design of a well-diversified portfolio crucially depends on a correct understanding of how closely international stock market returns are correlated. Changes in international correlation patterns call for an adjustment of portfolios. Policy makers are interested in correlations among equity markets because of their implications for the stability of the global financial system. The preparation of monetary policy is also affected by international stock market developments, due to the international propagation of shocks via equity markets, the wealth channel and confidence effects. The global trend towards a greater role of the stock market in the economy has made this kind of spillover more important. The academic literature on comovement among international equity markets is voluminous. Although there seems to be general agreement that correlations between equity markets are not constant over time, it is less clear whether correlations are actually trending upward.1 For instance, Roll (1989), surveying a number of papers published in the 1980s, concludes that the increase in international stock return correlations in the 1980s compared to the 1970s is only of a small magnitude. Similarly, King et al. (1994) find little support for a trend increase in correlations among stock markets for the 1970–1990 period. They conclude that authors who argue that markets have become increasingly integrated on the basis of data immediately around the crash in 1987 might confuse a transitory (i.e., around the crash) with a permanent increase in correlations.2 In contrast, Longin and Solnik (1995), who explicitly model the conditional multivariate distribution of international equity returns, are able to show that, for the period 1960–1990, correlations between stock returns in the US and in France, Switzerland, Japan, and the UK, respectively, have increased significantly. Furthermore, Rangvid (2001) conducts a recursive common stochastic trends analysis and is able to show that there is increasing convergence (in levels) among European stock markets. Lastly, Goetzmann et al. (2001) find that international equity correlations change dramatically through time, with peaks in the late 19th Century, the Great Depression, and the late 20th Century. Empirical tests for changes in correlation among equity returns usually involve some sort of two-step approach, where in the first step correlations are calculated over either fixed or moving subsamples, and in the second step the presence of level shifts or trends is assessed. These tests may suffer from two statistical deficiencies. First, Boyer et al. (1999) show that changes in correlations over time or across regimes cannot be detected reliably by splitting a sample according to the realized values of the data. Tests of changes in correlations are therefore often severely biased; see also Corsetti et al. (2001) and Forbes and Rigobon (2002). Put differently, it is not possible to assess the presence of an upward trend in correlations by looking at the (trending) behavior of subsample estimates of correlations. Instead, Boyer et al. (1999) argue, one should start with formulating a data-coherent model of the data generating process that includes the possibility of structural change, estimate the model's parameters, and then decide whether correlations have actually changed. A second statistical deficiency, which pertains particularly to the sample-splitting approach to testing for a change in correlation, is that such a test will lack power if the selected subsamples do not closely match the true correlation regimes. In this paper, we attempt to find out whether there has been a structural increase in the correlations among the stock markets of the US, the UK, Japan and Germany in the period 1980–2000. We seek to contribute to the existing literature in two ways. The first contribution is a novel procedure for evaluating structural change that avoids the weaknesses discussed above. We introduce a multivariate GARCH model with smoothly time-varying correlations, and derive a new test for constant correlation, building on the Lagrange Multiplier test developed by Tse (2000). Our setup allows us not only to endogenously determine the date of change, but also whether the transition to the new regime was abrupt or gradual. The second contribution of the paper is the focus on equity returns at the industry level, in addition to those at the aggregate level. We distinguish 10 sectors. The analysis of industry data enables us to investigate whether shifts in correlations are a broad-based phenomenon across industries. It might be the case that a specific group of sectors drives the movement towards greater international interdependence of stock returns. This part of the paper is related to the strand of the literature that explores whether differences in comovement of equity returns can be attributed to differences in industrial structure; see Griffin and Karolyi, 1998 and Heston and Rouwenhorst, 1994 and Roll (1992). The remainder of this paper is organized as follows. Section 2 discusses the data. Section 3 introduces the new multivariate GARCH model and develops the test for correlation constancy. Section 4 presents the empirical results. Section 5 contains a summary and some concluding remarks. Details on estimation and simulation evidence on the test for correlation constancy can be found in Appendix A and Appendix B, respectively.

In this paper, we focus on two important questions regarding the correlation among international equity returns. First, has there has been a structural increase in the degree of comovement among the world's most important stock markets – Germany, Japan, the UK and the US – over the past 20 years? And if so, at what moment did the change occur, and how long was the transition phase? Second, is the higher degree of comovement a broad-based phenomenon across industries, or is it possible to identify a group of sectors that appears to drive the process of deepening international stock market integration? To answer the two questions, we formulate a novel bivariate GARCH model for international equity returns with a smoothly time-varying correlation, and then derive a Lagrange Multiplier (LM) statistic to test the constant correlation hypothesis directly. Our procedure avoids the statistical deficiencies which often afflict other approaches in the literature, since both the date of change and the speed of the transition are endogenous. We apply the LM test to the stock market linkages among Germany, Japan, the UK and the US, using weekly stock prices for the market index and 10 industry indices between January 1980 and June 2000. Our main findings can be summarized as follows. Correlations among the German, UK and US stock markets have more than doubled, from around 0.30 to around 0.65 between 1980 and 2000. By contrast, correlations between the Japanese stock market and the other three markets have remained unchanged at 0.30 in this period. Correlation behavior at the aggregate level broadly reflects similar behavior at the industry level. Among Germany, the UK and the US, cross-country industry correlations have either gone up or remained the same, while for Japan the sectoral correlations overwhelmingly have not changed. There is no empirical evidence for the notion that a specific group of sectors plays a dominant part in the process of growing stock market integration. In short, we thus find a statistically significant broad-based increase in stock market comovement among Germany, the UK and the US, while the trend towards stock market integration seems to have bypassed Japan. Our estimation results point to a great variety in timing and speed of the correlation shifts across the bilateral stock market linkages, both at the market level and the industry level. For instance, the correlation between the returns on the market indices of the UK and the US gradually rose throughout the sample period, while that between the German and US markets increased sharply in the second half of the 1990s. This finding suggests that the structural shift towards a greater degree of comovement among international stock markets is not solely governed by global factors (such as advances in information technology, financial innovation and greater trade interdependence), but that country- and industry-specific factors also have a substantial impact. Relevant country-specific factors may be differences in transaction costs across exchanges and differences in information costs as a result of differences in listing requirements and accounting standards. The implications of our research for investors are that optimal portfolios have changed as a result of the correlation shifts. Because the correlations among the German, UK and US stock markets have greatly increased, whereas the correlations between Japanese stock market and the other three stock markets have not, the weight of Japanese stocks in the optimal portfolio has tended to increase over time at the expense of German, UK and US stocks.27 For policy makers, significantly higher correlations mean that equity market disturbances in one country are more likely to be transmitted to other countries, which may have adverse consequences for the stability of the global financial system. International stock market spillovers have also become more significant as the link between stock market and real economy has intensified, for example because of greater share holdings by households. Our finding of widely varying dates and speeds of structural change is a strong reminder that a flexible approach to modeling structural change really pays dividends. This is an important lesson for future research. However, our methodology still contains some important restrictive elements, in particular the strict monotonicity of correlation change. Relaxing these restrictions is an interesting topic for future research. Within our basic setup, monotonicity can be replaced by richer time-patterns in two ways. The first one is the introduction of more than two correlation regimes, which allows hump-shaped patterns. The second one is not to use time as the transition variable, but a measure of interdependence, for instance international trade patterns. As such variables may not be necessarily monotonic, this also introduces the possibility of non-monotonic change. An additional advantage of this approach is that it may shed some light on the underlying causes of long-run changes in the degree of stock market comovement. Finally, a natural extension of our analysis is to estimate a single multivariate STC-GARCH model instead of a series of bivariate STC-GARCH models.