In allocating and managing risk across global markets, it is crucial to take account of the interrelationships between different markets. For example, efficient hedging or asset allocation strategies must recognize that different markets are linked--albeit in complex ways.
Although one can analyze these relationships by looking at correlations, there are some practical obstacles. First, the full correlation matrix is hard to interpret, since it contains so much information. Second, individual historical correlations tend to be unstable over time. Third, correlation analysis does not let us abstract away from individual markets, to identify underlying global risk factors that drive market shifts across different markets.
However, it is possible to extract 'independent risk factors' from a correlation matrix as follows: the risk factors correspond to the eigenvectors of the matrix, and the importance of a risk factor is measured by the size of the corresponding eigenvalue. This is known as principal components analysis. In practice, a few eigenvalues dominate the rest, so only the first one to three eigenvectors are meaningful. Thus, the method extracts a small number of dominant risk factors from the entire correlation matrix.
This is a well-established technique in historical yield curve analysis. In almost all bond markets the first two eigenvectors correspond to a nearly parallel shift in the yield curve and a shift in the slope of the curve; the remaining eigenvectors tend not to be statistically significant. That is, in any individual bond market the main sources of risk are parallel risk and slope risk, which together explain 90%95% of shifts in bond yields. This conclusion is extremely robust, and independent of the historical period used.
A principal components analysis of correlations between world equity markets in the period 19701995 shows there are two dominant risk factors: a global shift across all markets, explaining 52% of market moves, and a shift in Asian markets (including Australia) relative to Continental Europe, explaining a further 15%. The 1997 data gives similar results: the dominant factors are a global shift and a shift in Asian versus Mediterranean markets, though the latter is now less significant.
Passing to world bond markets, the graph shows the dominant global risk factor, where the periods 197379, 198089 and 199097 have been analyzed separately. It illustrates the point that results of the analysis can change as markets evolve. In each case, the dominant factor is a global shift in bond yields. However, there is evidence of increasing integration of bond markets over time. In particular, this single risk factor is, relatively, much more important in the 1990s than it was in the 1970s, and some specific markets which were not linked into this risk factor in the 1970s, such as Australia and France, are linked in the 1990s. Also, in the 1990s a second dominant factor emerges: a shift in dollar bloc yields relative to Continental Europe.
For world short-term interest rates the results are quite different. Again the dominant risk factor is a parallel shift in rates across different markets. But it has never explained more than 30% of movements in official rates; and, whereas in the 1970s it was a shift across all markets, by the 1990s various markets, such as France, Canada and Australia, have become de-coupled from this risk factor. So here the analysis reaches much weaker conclusions. This is probably because official rates are strongly influenced by domestic politics in individual countries, in contrast to world equity and bond markets which are more closely linked to global economic fundamentals.
Finally, for foreign exchange markets the analysis produces consistent conclusions when applied to the 1970s, 1980s and 1990s. In each case the dominant factor, explaining 50%65% of exchange rate movements, is a shift in dollar bloc currencies relative to Europe and Japan. The second and third most important factors correspond to changes in cross rates within the dollar bloc.
Although the analysis is easy to carry out, it must be applied with care. As illustrated above, the results can be sensitive to the historical period used. They also depend on the countries included in the dataset, so if emerging markets data were added, the set of dominant factors would change. And often one must use market insight, and not just statistics, to decide whether a particular eigenvector corresponds to a meaningful risk factor and is not just the product of statistical noise. Finally, as with any analysis of historical data, the results need not apply to the future. For example, European monetary union may well affect the nature of the dominant global risk factors. However, there is already strong evidence of European integration in the results for currency and bond markets.
Principal components analysis is clearly a powerful tool, but one that must be carefully tailored to the nature of a specific investor's global exposure. Different market participants will tend to apply it in different ways.
This week's Learning Curve was written byWesley Phoa,Los Angeles-based director of research atCapital Management Sciences.