EUR/JPY and USD/CHF 2004-2008: EUR/JPY is the leader.

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Written by Forex Automaton   
Tuesday, 30 December 2008 15:30

The two exchange rates with the same sign of the interest rate differential, Euro/Japanese Yen and US Dollar/ Swiss Franc turn out to be negatively correlated. Studied on the hour time scale, the correlation looks highly asymmetric, making EUR/JPY look like the leader and CHF/USD (not USD/CHF, due to the negativeness of the correlation) -- the follower. The necessary caveat is that this is a time-integrated picture.

EUR/JPY and USD/CHF volatility comparison

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

currency pair time scale Asia-Pacific session European session American session
EUR/JPY hour 1.2×10-3 1.3×10-3 1.3×10-3
USD/CHF hour 1.1×10-3 1.5×10-3 1.4×10-3

Fig.1 and Table 1 show that volatilities of USD/CHF and EUR/JPY are comparable. Volatilities of both exchange rates depend on the trading session and are at the minimum during the Asia-Pacific 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/JPY 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 -0.23 -0.22 -0.16

EUR/JPY and USD/CHF form a negatively correlated combination. This is a rare case when the trading session with lower volatility (and presumably lower volume), the Asia-Pacific trading session, shows somewhat higher correlation amplitude.

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

Fig.2: Cross-correlation of EUR/JPY 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/JPY 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. The lagged correlation, manifested through the considerable non-zero amplitude at the -1 hour time lag, is significant only in the European and American trading. The Asia-Pacific session is generally poor in predictive correlations. A comparison with the same analysis performed repeatedly on the random data designed to mimic volatilities of EUR/JPY and USD/CHF lets one estimate the accuracy of the correlation measurements, see Fig.3 below.

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

Fig.3: Cross-correlation of EUR/JPY 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/JPY 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 peak asymmetry is to the left, into the area of negative lags (wherby CHF/USD would be lagging behind EUR/JPY). The reason negative lags are interpreted this way is the definition: the lag td is defined as

td = t1 - t2,

where index "1" denotes EUR/JPY and index "2" denotes USD/CHF. Therefore, negative correlation value at negative lags means that movements of the same direction in EUR/JPY and CHF/USD happen at an earlier time in EUR/JPY, or EUR/JPY is leading and CHF/USD is following. This is strange for the historic period most of which was marked by relatively high interest rates in the US and Europe, while both JPY and CHF played the role of carry-trader funding currencies. The analysis of CHF/JPY and USD/CHF combination led to the similarly paradoxical conclusion: CHF/JPY was found to lead and CHF/USD to follow. In the other combination involving JPY, AUD/JPY and USD/CHF, the effect was absent. 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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