EUR/GBP and EUR/CHF 2002-2008: negative correlation underscores importance of interest rates

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Written by Forex Automaton   
Wednesday, 24 September 2008 10:49

The cross-rates Euro/Pound Sterling and Euro/Swiss Franc form a remarkable combination of world's two historically least volatile floating exchange rates. They are weakly negatively correlated, despite the fact that both are EUR-based exchange rates. When looked at on an hour time scale, the correlation appears to be localized at the zero time-lag and thus presents no interest from the short-range forecasting point of view.

EUR/GBP and EUR/CHF volatility comparison

Fig.1: comparing volatilities of hour-by-hour logarithmic returns in EUR/GBP (top panel) and EUR/CHF (bottom panel) for the three trading sessions: Asia-Pacific session, European session, and the American session. The sessions are defined in New York time to be at least 12 hour long each. The histograms are normalized distributions of logarithmic returns.

Table 1: Hour-by-hour volatilities (RMS) for the time series of logarithmic returns in EUR/GBP and EUR/CHF in various trading sessions in 2002-2008.

currency pair time scale Asia-Pacific session European session American session
EUR/GBP hour 0.76×10-3 0.93×10-3 0.79×10-3
EUR/CHF hour 0.45×10-3 0.55×10-3 0.49×10-3

Fig.1 and Table 1 show that the volatilities of EUR/GBP and EUR/CHF are similar, the two being the least volatile floating exchange rates. As always in forex, at least on the 1-hour time scale considered, the distributions of logarithmic returns are not "bell-shaped", they are strongly non-Gaussian. The distributions look roughly triangular on the log scale. Therefore a lot more appropriate model for the tails would be an exponent, meaning the returns themselves (not the logarithms) follow a power law.

Table 2: Pearson correlation coefficient for the time series of logarithmic returns in EUR/GBP and EUR/CHF in various trading sessions in 2002-2008. Time frames of the sessions are shown in New York time.

time scale Asia-Pacific session European session American session
hour -0.0056 -0.034 -0.033

EUR/GBP and EUR/CHF form a weakly negatively correlated combination, despite the fact that EUR is present as a base currency in both rates. It is noteworthy that the Asia-Pacific traders are "unaware" of the correlation -- it is not seen in that time zone.

EUR/GBP and EUR/CHF intermarket correlation 1 hour time-lag bin

Fig.2: Cross-correlation of EUR/GBP and EUR/CHF, derived from the hour-by-hour logarithmic returns, for the three trading sessions. Time frames of the sessions are shown in New York time.

Fig.2 presents the cross-correlation of EUR/GBP and EUR/CHF over the time lag (hours), for the various trading session (time zones). There is no interesting features to talk about in the vicinity of the zero time-lag bin where the predictive tails of the correlation peak are usually located, meaning that the correlation is tightly localized (or in other words, response happens quickly). A comparison with the same analysis performed repeatedly on the random data designed to mimic volatilities of EUR/GBP and EUR/CHF lets one estimate the accuracy of the correlation measurements, see Fig.3 below.

EUR/GBP and EUR/CHF intermarket correlation 1 hour time-lag bin with uncertainty estimate

Fig.3: Cross-correlation of EUR/GBP and EUR/CHF for the European (Eurasian) trading session shown against the backdrop of statistical noise (red). The noise is obtained from martingale simulations based on the recorded volatilities of EUR/GBP and EUR/CHF in this trading session for the period under study. The noise is presented as mean plus-minus 1 RMS, where RMS characterizes the distribution of the correlation value obtained for each particular bin by analyzing 20 independent simulated pairs of uncorrelated time series.

Fig.3 demonstrates the non-flat (although quite predictable) behaviour of the noise level with time lag, caused by the constraint on the time lags associated with the definition of the trading session time window. This can not be ignored otherwise one risks over-interpreting the picture. The area around zero is fairly safe since the noise is at the minimum when the lag is at an integer number of days. Naturally, as the random model responsible for the noise (red background in the figure) does not contain any correlation between the two exchange rates, it shows no correlation peak at the zero time lag.

Difference between s/n-o/n EUR LIBOR and GBP LIBOR historical 2002-2008 Difference between s/n-o/n EUR LIBOR and CHF LIBOR historical 2002-2008

Fig.4. Top: difference between s/n-o/n (spot/next-overnight) EUR and GBP LIBOR rates (EUR-GBP). Bottom: difference between s/n-o/n (spot/next-overnight) EUR and CHF LIBOR rates (EUR-CHF). Vertical scale unit is 1%. Based on historical LIBOR interest rates data for 2002-2008. Time axes are labeled in the MM-YY format.

You might expect (based on simple calculus) that because EUR/GBP and EUR/CHF share the same base currency, EUR, they should be positively correlated. That is not the case and the negativeness of the correlation illustrates importance of the LIBOR rates in setting the agenda in the forex markets. As Fig.4 shows, the interest rate differential between EUR and GBP has been historically strongly in favor of GBP, (negative EUR-GBP data in Fig.4, top panel) whereas between EUR and CHF, it is in favor of EUR (positive EUR-CHF data in Fig.4, bottom panel.) Thus, market dynamics beats the naive calculus.

The data used are from the period 2002-08-20 00:00:00 to 2008-02-01 00:00:00.

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