TABLE 10.3 Means, variances, maxima and minima of correlation.

Means, variances, maxima and minima of the linear correlation coefficients as shown in Figures 10.2 through 10.7. For each pair of financial instruments, four correlation intervals T/N of decreasing size are investigated. The total sampling period T is from January 7, 1990, to January 5, 1997.

1990 1992 1994 1996 Time (year)

usd/dem - usd/nlg

1990

1992 1994 1996 Time (year)

usd/dem - usd/nlg

1

1990

1992 1994 Time (year)

1996

1990

1992 1994 Time (year)

1996

FIGURE 10.2 Linear correlation coefficients calculated using increasingly small sub-intervals, T/N = (365 days, 128 days, 32 days, and 7 days), for the FX return pair USD-DEM - USD-NLG. The dashed lines above and below zero correlation are 95% confidence ranges assuming normally distributed returns.

correlation stability. The highly correlated USD-DEM - USD-NLG returns shown in Figure 10.2 appear largely constant over the total sample period of 7 years. As the subperiod width for correlation calculation decreases (and the number of correlation calculations inside the total period increases), more structure becomes apparent. This additional structure is reflected by an increasing variance in Table 10.3. Correlations calculated with lower data frequency are not simply an average of those calculated with higher quotation frequencies; Table 10.3 shows the mean value for USD-DEM - USD-NLG correlations moving steadily downward with increasing correlation resolution (an -11% change between yearly data resolution and weekly resolution). This can be partially explained by considering that error distributions for empirically computed correlations are not symmetric when coefficients differ from zero. However, such drops in correlation with higher data frequency as can be observed with the DJIA-Amex pair point to a stronger effect which will be addressed in more detail in Section 10.5.

usd/dem - usd/nlg usd/dem - usd/nlg

usd/dem - usd/gbp

1990 1992 1994 1996 Time (year)

usd/dem - usd/gbp

1990

1992 1994 Time (year)

1996

usd/dem - usd/gbp

1990 1992 1994 1996 Time (year)

usd/dem - usd/gbp

1990 1992 1994 1996 Time (year)

FIGURE 10.3 Linear correlation coefficients calculated using increasingly small sub-intervals, T/N = (365 days, 128 days, 32 days, and 7 days), for the FX return pair USD-DEM - USD-GBP. The dashed lines above and below zero correlation are 95% confidence ranges assuming normally distributed returns.

Figures 10.3 and 10.4 show correlations for the FX rate pairs USD-DEM -USD-GBP and USD-DEM - USD-ITL. Note that the inverse rate USD-GBP was used instead of the more usual GBP-USD, in order to be in line with other currencies and to obtain positive correlation. Both figures exhibit fast and large drops in correlations during the second and third weeks of September 1992. Presumably, this directly reflects the turmoil of the European Monetary System (EMS) at that time, when GBP and ITL left the system. This appears to be a clear example of correlation breakdown.

Recapitulating the major points of Section 10.4, correlation was examined as a function of time for a number of different financial instruments. The time frame of 7 years was divided in four different ways, using subperiods of 365, 128, 32, and 7 days. The number of subperiods over the total 7 year period was then 7,19,79, and 365, respectively. The subperiods of different size were divided into n intervals for return observations. This number had roughly the same size in all cases,