EUR/GBP and USD/CHF 2004-2008: "trivial" intermarket correlation

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Written by Forex Automaton   
Monday, 29 December 2008 15:44

The two exchange rates with the opposite signs of the interest rate differential, Euro/Pound Sterling and US Dollar/ Swiss Franc and negatively correlated. The correlation, when studied on the hour time scale, seems too tight to offer forecasting potential. Such simple one-peak structures centered at the zero time-lag are called "trivial correlations" in this series of analysis notes. The necessary caveat is that this is a time-integrated picture.

EUR/GBP and USD/CHF volatility comparison

Fig.1: comparing volatilities of hour-by-hour logarithmic returns in EUR/GBP (top panel) and USD/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 USD/CHF in various trading sessions in 2004-2008.

currency pair time scale Asia-Pacific session European session American session
EUR/GBP hour 0.78×10-3 0.92×10-3 0.74×10-3
USD/CHF hour 1.1×10-3 1.5×10-3 1.4×10-3

Fig.1 and Table 1 show that USD/CHF is considerably more volatile. Volatilities of both exchange rates depend on the trading session and are at the peak during the European session. 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, with pronounced tails.

Table 2: Pearson correlation coefficient for the time series of logarithmic returns in EUR/GBP and USD/CHF in various trading sessions in 2004-2008. Time frames of the sessions are shown in New York time.

time scale Asia-Pacific session European session American session
hour -0.34 -0.35 -0.38

EUR/GBP and USD/CHF form a negatively correlated combination. The trading session with lower volatility (and presumably lower volume), the Asia-Pacific trading session, is also the one with the lower correlation amplitude.

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

Fig.2: Cross-correlation of EUR/GBP and USD/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 USD/CHF over the time lag (hours), for the various trading session (time zones). The difference of the zero time lag peaks among the different time zones (hidden from view in the figure) is best discussed in terms of the Pearson correlation coefficients (normalized variance, Table 2), the variance here being with good accuracy the zero-lag correlation amplitude. A comparison with the same analysis performed repeatedly on the random data designed to mimic volatilities of EUR/GBP and USD/CHF lets one estimate the accuracy of the correlation measurements, see Fig.3 below.

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

Fig.3: Cross-correlation of EUR/GBP and USD/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 USD/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 feature at the zero time lag. The word of caution is in place: this is a time-averaged picture and an in-depth study of a time evolution of this picture may turn out to be more informative. This is the subject of a special section on the time evolution of forex inefficiencies.

The data used are from the period 2004-04-01 00:00:00 to 2008-10-01 00:00:00.

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