Dispersion as Cross-Sectional Correlation

We introduce the concept of cross-sectional dispersion of stock market returns as an alternative to the time-series approach to estimating the global correlation level of equity markets. Our objective is to derive a simple, instantaneous measure of the general level of global market correlation. Our cross-sectional method of estimating global correlation is dynamic and, using cross-sectional data, gives instantaneous information on the trend of global correlation. The traditional time-series method requires a long period of observations, and overlapping data have to be used to study the change in correlation. Both methods yield similar estimates for a “long” period, however, so a combination of the cross-sectional and time-series approaches should be of practical use to global asset managers. We introduce a new approach to estimating the global correlation of stock markets that has as the key ingredient the cross-sectional dispersion of stock market returns. The simple model of global market correlation is based on the postulate that each country has a beta of 1 relative to the world market. This model allows one, in a simple manner, to derive global correlation from the dispersion, and it also implies that global correlation is inversely proportional to dispersion. On the basis of the model, we show how to estimate the global market correlation by using cross-sectional (contemporaneous) short-term data. An important aspect is that the model allows derivation of an instantaneous measure of the general level and trend of global market correlation. The issue of changes in global correlations has strong practical relevance. Investment managers optimize their asset allocations partly on the basis of the international covariance of market returns. The level of global correlation affects the degree of diversification needed in investment portfolios. It also has a bearing on the extent of profit opportunities available to active asset allocators. What managers need is an indicator that will instantaneously track the time variation in global correlation—especially when market volatility is high, because the globalization of investments and the instantaneous flow of information have made crises contagious. By providing instantaneous detection of changes in correlation, our dispersion indicator and the global correlation measure derived from it are practical, even if partial, tools to meet this need. The traditional time-series method requires a long observation period and overlapping data (moving windows) in order for the change in correlation to be studied. Thus, it yields a slow-moving estimate of the level of global correlation that is poorly suited to rapid detection of changes in global correlations. Because our dispersion-based correlation uses only contemporaneous data, estimates at two successive points in time use independent data sets; therefore, changes in the global correlation level can be detected immediately. The two methods yield similar estimates when data over a long (five-year or more) period are used. We illustrate the concept of dispersion by reporting a study of its estimated values from January 1971 to September 1998 for a set of developed market indexes. We found that the dispersion was quite stable over the period, at an average of 4.5 percent a month or 15.6 percent annually but that the dispersion has had a tendency to decrease with time, which suggests more integrated equity markets. We then report results for using the model to derive the global correlation level from the dispersion for the same equity markets and period. We found that correlation has had a positive trend, increasing from 66 percent at the beginning of 1971 to 74 percent in September 1998, but that the slope of the regression is quite weak. These findings suggest that the developed equity markets have been becoming more integrated but at a slower pace than some analysts believe. We make no conclusions about whether global investment should be conducted along country lines or industry lines. But our approach could be extended to detect valid asset classes: groupings of stocks that have large covariance between them and small covariance within them.