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100 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. Instrument  Correlation  Mean  variance   Min.  pair  period  value  (a2)    USDDEM  USDNLG  1 year  0.99  0.000026  0.99  0.98  USDDEM  USDNLG  128 day  0.99  0.00012  1.00  0.95  USDDEM  USDNLG  32 day  0.96  0.0029  1.00  0.54  USDDEM  USDNLG  7 day  0.88  0.0067  0.98  0.41  USDDEM  USDGBP  1 year  0.76  0.029  0.96  0.42  USDDEM  USDGBP  128 day  0.79  0.015  0.98  0.57  USDDEM  USDGBP  32 day  0.76  0.031  0.98  0.09  USDDEM  USDGBP  7 day  0.69  0.030  0.97  0.20  USDDEM  USDITL  1 year  0.76  0.040  0.99  0.41  USDDEMUSDITL  128 day  0.75  0.057  0.99  0.18  USDDEM  USDITL  32 day  0.76  0.044  0.99  0.07  USDDEM  USDITL  7 day  0.68  0.044  0.97  0.07  DJIA  AMEX  1 year  0.73  0.0083  0.84  0.60  DJIA  AMEX  128 day  0.70  0.0087  0.85  0.57  DJIA  AMEX  32 day  0.41  0.041  0.78  0.29  DJIA  AMEX  7 day  0.01  0.030  0.62  0.50  DEM 36m  DEM 912m  1 year  0.84  0.00074  0.88  0.81  DEM 36mDEM 912m  128 day  0.78  0.0084  0.90  0.57  DEM 36mDEM912m  32 day  0.71  0.025  0.96  0.13  DEM 36mDEM912m  7 day  0.54  0.074  1.00  1.00  USD 36m  DEM 36m  1 year  0.33  0.024  0.51  0.13  USD 36m  DEM 36m  128 day  0.30  0.028  0.59  0.10  USD36mDEM 36m  32 day  0.30  0.051  0.85  0.34  USD 36m  DEM 36m  7 day  0.28  0.066  1.00  0.52 
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 subintervals, T/N = (365 days, 128 days, 32 days, and 7 days), for the FX return pair USDDEM  USDNLG. The dashed lines above and below zero correlation are 95% confidence ranges assuming normally distributed returns. correlation stability. The highly correlated USDDEM  USDNLG 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 USDDEM  USDNLG 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 DJIAAmex 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 subintervals, T/N = (365 days, 128 days, 32 days, and 7 days), for the FX return pair USDDEM  USDGBP. 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 USDDEM USDGBP and USDDEM  USDITL. Note that the inverse rate USDGBP was used instead of the more usual GBPUSD, 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,
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