Swiss Franc (CHF) LIBOR: technical predictability overview

I’ve outlined the original motivation to study historical LIBOR data from predictability point of view in the USD LIBOR article. I continue with the logarithmic returns technique that proved useful in forex. Like the previous reports, this document begins with historical LIBOR charts for the Swiss Franc, continues with volatility analysis, and culminates with autocorrelations and correlations. You will see that predictable patterns in CHF LIBORs vary with duration term. Autocorrelations of short-term LIBORs show fast (about 4-day period) oscillation. For 3-month and 6-month terms, the main correlation pattern does not develop 70-day period waves on top of positive background, in contrast to USD and EUR LIBORs, but keeps oscillating between positive and negative autocorrelation values, with the oscillation period longer than that of the shorter terms. The autocorrelation of 12-month LIBOR remains similar to 6-month instead of becoming more uniformly positive as it does for JPY or more jittery as it does for USD, EUR and GBP.

LIBOR charts

History of s/n-o/n CHF LIBOR 2002-2008 History of 1 week CHF LIBOR 2002-2008 History of 1-month CHF LIBOR 2002-2008 History of 3-month CHF LIBOR 2002-2008 History of 6-month CHF LIBOR 2002-2008 History of 12-month CHF LIBOR 2002-2008

Fig.1: Historical CHF LIBOR rates charts, top to bottom: s/n-o/n, 1-week, 1-month, 3-month, 6-month and 12-month. Time axis is labeled in MM-YY format.

The evolution of visual features with maturity here resembles that of other currencies, except for the fact that for CHF, longer maturities show considerably less “initiative” in developing their own trends. Their history looks more like a dumb version of the shorter ranges. For the short maturities, the markets jump the gun trying to anticipate the course of events almost regularly, to the extent this nervousness must represent a regular and significant speculative opportunity, if the market instruments tied to the LIBOR rates have the same features. This will be seen qunatitatively in the correlation plots.

LIBOR volatility

Table 1: Day-by-day volatilities (RMS) for the time series of logarithmic returns in CHF LIBOR in 2002-2008, various maturities

durationtime scalevolatility (RMS)
s/n-o/nday7.3×10-2
weekday4.8×10-2
monthday2.6×10-2
3 monthsday2.2×10-2
6 monthsday2.2×10-2
12 monthsday2.4×10-2

Volatility of CHF LIBOR seems to go down with duration in a more reliable fashion than for other currencies, in particular, USD and EUR. Like JPY, logarithmic returns in CHF look very volatile — this is because the market think about interest rate variations in the “absolute”, not relative sense, and because JPY and CHF interest rates are low, therefore interest rate moves worthy of market’s attention are relatively large for these markets.

Distribution of logarithmic returns in s/n-o/n and 1-week CHF LIBOR rates Distribution of logarithmic returns in 3-month, 6-month and 12-month CHF LIBOR rates

Fig.2: Distributions of logarithmic returns in CHF LIBOR rates, top: s/n-o/n and 1-week, bottom: 1-month, 6-month and 12-month maturity. Volatility is a measure of the width of the return distribution.

The distribution of logarithmic returns look broader than power-law. Remember that with returns already containing logarithm and with the vertical axis explicitly logarithmic, we are looking at what is effectively a log-log plot, where any power law dependence would have looked linear, with different power law exponents resulting in different slopes.

LIBOR autocorrelations

As with some of the most volatile forex exchange rates and all LIBORs looked at so far, the most prominent feature of the s/n-o/n and 1-week CHF LIBOR autocorrelations is the “bipolar disorder” pattern seen from the bins with large negative signal surrounding the zero-time lag bin. (The expression “bipolar disorder” in relation to the market is credited to Benjamin Graham). Continuing with the psychiatric analogy, these indicate rapid (next day or two, depending on LIBOR term) changes in the mood of the credit market, a price action followed by an immediate correction.

CHF s/n-o/n LIBOR autocorrelation, 1 day time scale CHF 1-week LIBOR autocorrelation, 1 day time scale CHF 1-month LIBOR autocorrelation, 1 day time scale CHF 3-month LIBOR autocorrelation, 1 day time scale CHF 6-month LIBOR autocorrelation, 1 day time scale CHF 12-month LIBOR autocorrelation, 1 day time scale

Fig.3:Autocorrelation of logarithmic returns in the historical CHF LIBOR is shown against the backdrop of statistical “noise”. The noise is obtained from martingale simulations based on the historical volatilities of LIBOR 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 time lag bin by analyzing 20 independent simulated uncorrelated time series. The RMS is a measure of accuracy in the determination of the correlation values, an irreducible uncertainty dependent on the amount of data and the time scale. Top to bottom: s/n-o/n, 1-week, 1-month, 3-month, 6-month, and 12-month data.

Fig.3 and subsequent figures ascertain the significance of the patterns by comparing with the statistical noise estimate, based on simulations devoid of correlations, but with volatility of the actual data. 1-month and longer term LIBOR autocorrelations have broad peaks around zero. This is very different from forex exchange rates, and implies that in LIBOR, medium-range (several days) forecasting is straighforward for these maturities: betting on the continuation of a trend is the winning strategy. In other words, trend following is possible with medium-range LIBOR.

The predictive positive zero-lag peak of 1-month and longer maturities has to be contrasted with the opposite feature seen in shorter maturities, namely the “bipolar disorder”, a tendency to form patterns where the strategy of betting on the trend reveral is more likely to succeed. This tendency shows up in the negative correlation magnitude at the lag that corresponds to the time it takes for the trend reversal. In CHF LIBOR, s/n-o/n and 1-week data, the time is no more than 2-3 days. Trend following is not a viable strategy with s/n-o/n and 1-week LIBOR: here, betting on the next-day trend reversal or using longer range correlations, some of which just as sharp, seems to be the surest strategy.

Cross-correlations of LIBOR terms

Next, I am going to look at correlation between LIBOR rates of different maturities for various time lags. These help answer the question to what extent one LIBOR term can be predicted on the basis of any others. The zero-lag correlation magnitudes between different LIBOR terms are presented as Pearson correlation coefficents in the table. The figures focus on the correlation shapes at the time lags surrounding the zero-lag peak.

Table 1: Pearson correlation coefficients between CHF LIBOR in 2002-2008, various maturities

durations/n-o/n1-week1-month3-month6-month12-month
s/n-o/n10.730.510.320.250.17
1-week10.620.460.350.28
1-month10.770.660.51
3-month10.850.66
6-month10.85
12-month1

The correlation of different maturity terms (which is roughly the square root of the zero time-lag peak amplitude) is seen to go down as the difference in maturities grows; similar maturities are correlated tighter. Overall, the evolution with LIBOR maturity term is the same as described for autocorrelations.

Correlations between s/n-o/n and longer term LIBOR rates

Correlation between logarithmic returns in s/n-o/n and 1-week CHF LIBOR rates as a function of time lag, days Correlation between logarithmic returns in s/n-o/n and 1-month CHF LIBOR rates as a function of time lag, days Correlation between logarithmic returns in s/n-o/n and 3-month CHF LIBOR rates as a function of time lag, days Correlation between logarithmic returns in s/n-o/n and 6-month CHF LIBOR rates as a function of time lag, days Correlation between logarithmic returns in s/n-o/n and 12-month CHF LIBOR rates as a function of time lag, days

Fig.4: Correlation between logarithmic returns in s/n-o/n and, top to bottom: 1-week, 1-month, 3-month, 6-month and 12-month CHF LIBOR rates as a function of time lag, days, shown against the backdrop of statistical noise (red). The noise is obtained from martingale simulations based on the historical LIBOR volatilities 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 uncorrelated time series.

Correlations between 1-week and longer term LIBOR rates

Correlation between logarithmic returns in 1-week and 1-month CHF LIBOR rates as a function of time lag, days Correlation between logarithmic returns in 1-week and 3-month CHF LIBOR rates as a function of time lag, days Correlation between logarithmic returns in 1-week and 6-month CHF LIBOR rates as a function of time lag, days Correlation between logarithmic returns in 1-week and 12-month CHF LIBOR rates as a function of time lag, days

Fig.5: Correlation between logarithmic returns in 1-week and, top to bottom: 1-month, 3-month, 6-month and 12-month CHF LIBOR rates as a function of time lag, days, shown against the backdrop of statistical noise (red). The noise is obtained from martingale simulations based on the historical LIBOR volatilities 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 uncorrelated time series.

Correlations between 1-month and longer term LIBOR rates

Correlation between logarithmic returns in 1-month and 3-month CHF LIBOR rates as a function of time lag, days Correlation between logarithmic returns in 1-month and 6-month CHF LIBOR rates as a function of time lag, days Correlation between logarithmic returns in 1-month and 12-month CHF LIBOR rates as a function of time lag, days

Fig.6: Correlation between logarithmic returns in 1-month and, top to bottom: 3-month, 6-month and 12-month CHF LIBOR rates as a function of time lag, days, shown against the backdrop of statistical noise (red). The noise is obtained from martingale simulations based on the historical LIBOR volatilities 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 uncorrelated time series.

Correlations between 3-month and longer term LIBOR rates

Correlation between logarithmic returns in 3-month and 6-month CHF LIBOR rates as a function of time lag, days Correlation between logarithmic returns in 3-month and 12-month CHF LIBOR rates as a function of time lag, days

Fig.7: Correlation between logarithmic returns in 3-month and, top to bottom: 6-month and 12-month CHF LIBOR rates as a function of time lag, days, shown against the backdrop of statistical noise (red). The noise is obtained from martingale simulations based on the historical LIBOR volatilities 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 uncorrelated time series.

EUR/CHF 2002-2008: Predictability Overview

The Euro / Swiss Franc in 2002-2008 is a currency pair with relatively low volatility. In the medium term (days and weeks), dynamics of EUR/CHF is visibly more random than one would expect on the basis of its long range behaviour — a feature not seen with more volatile currency pairs before.

The interest rate differential has been in favor of the Euro.

The basic autocorrelation

EUR/CHF correlation 1 hour time-lag bin

Fig.1: Autocorrelation of hourly logarithmic returns in EUR/CHF. The time lag is in “business time” (periods without update ticks are excluded). The red band shows the level of noise as iferred from martingale simulations (see text).

As before we employ autocorrelation as a straightforward, inter-disciplinary, non-proprietary technique to test market efficiency in the EUR/CHF market. In Fig.1 we look for features on the time scale of up to two days such as to suit the time scale of day trading or swing trading. The hatched red band shows the range of statistical noise (namely its expectation plus minus its RMS deviation). Statistical noise was obtained by simulating 20 independent time series of the length corresponding to that of the EUR/CHF series, each one constructed to reproduce the measured distribution of returns for the time period under study, but completely devoid of correlations ( martingale time series). From these, the expectation and RMS or the autocorrelation amplitude in each time lag bin were calculated. The one-hour time lag “contrarian” feature (a significant anticorrelation) we saw in this type of plot for other currency pairs involving CHF ( CHF/JPY) and EUR ( EUR/AUD ) is quite strong in the EUR/CHF autocorrelation. The autocorrelation being an average of a product of hourly returns taken with a lag, this negativity means that we are way too frequently (more frequently than in the corresponding martingale time series) taking a product of opposite sign returns for this time lag— or that the product of the opposite sign returns by far outweighs that of the same sign returns for this time lag. Because trend reversals on the time scale of about one hour happen either too often or are too lucrative, EUR/CHF, like EUR/AUD, GBP/JPY, AUD/USD and AUD/JPY analyzed before, may well be the market where winning strategy requires being a contrarian on a short time scale.

EUR/CHF is the currency pair where the martingale simulation “prescribes” an overall positive correlation — a feature which we have not seen pronounced so strongly with other currency pairs in this series of reviews. Its visibility is underscored by the overall relatively low volatility of EUR/CHF with consequently tighter noise range (width of the red band in the figures). The autocorrelation for the lag ranges we have probed is inconsistent with such a “prescription”. Therefore, short range dynamics of EUR/CHF is quite different from what is prescribed by its long term “investment theme”. As always, one should not trade this pair short-range on the basis of long-range considerations alone.

EUR/CHF correlation 4 hour time-lag bin

Fig.2: EUR/CHF autocorrelation as in Fig.1, but with time lag bin increased to 4 hours.

24-hour trading cycle.

EUR/CHF bullish and bearish autocorrelation

Fig.3: EUR/CHF bullish and bearish autocorrelations. Yellow: correlating only positive hourly returns. Blue: correlating only negative hourly returns.

In Fig.3 we construct autocorrelations of the subsamples of the full time series (the “bullish” and “bearish” ones) selected by taking only positive and negative returns respectively. The 24 hour cycle of bullish and bearish action is again clearly seen as the maxima of the correlation are located at multiples of the 24 hour lag: 24, 48, 72, 96, 120 hours and so on. Therefore, smart trend following means something more than following a trend that existed in the near past. It means following a trend that existed this time of the day yesterday, the day before yesterday, and so on — that gives you better than average chance of winning! Conversely, buying because the currency went up 12 hours ago (or selling because it went down 12 hours ago), all the rest being equal, is the least recommended strategy. (See why this 24-hour correlation feature alone is not a prediction strategy. ) Needless to say, this effect is not present in the simulated martingale data.

Note that whether this trend following pattern in all time zones is equally strong is a question that requires a separate study focusing on the best time zones for trend following in EUR/CHF.

EUR/CHF bullish and bearish autocorrelation long range

Fig.4: EUR/CHF bullish and bearish autocorrelations. Axes and color codes as in the previous figure. Range expanded compared to the previous figure to show the characteristic time length of this market memory effect.

Similar patterns have been seen before with most other currency pairs in this series of predictability reviews. It is interesting to note that typically, the “bearish” correlation has higher amplitude whenever the base currency commands a higher interest rate. This has been seen with AUD/USD, AUD/JPY, USD/JPY, GBP/JPY, USD/CAD, (although the interest rate differential has not been that high, it is in favor of USD), AUD/USD, CHF/JPY. In case of EUR/AUD where the interest rate differenctial favors the quote currency, the “bullish” correlation is stronger. These two observations can be summarized in one sentence: the closing of long positions in a high yield currency can be a correlated and thus a relatively predictable process. While in the case of classic carry-trade currency pairs such as AUD/JPY this has been associated with the unwinding of the carry-trade, the underlying mechanism is likely to be similar for other currency pairs. The case of EUR/CHF is unlikely to be an exception, and indeed EUR commands an interest-rate premium with respect to CHF for the period under study.

The fact that one can read the sign of interest rate differential off the public forex quotes via basic correlation analysis indeed goes against the efficient market dogma as it indicates that despite large liquidity such interest rate differentials are not completely discounted by the markets and there remain profit opportunities for algorithmic trading.

Summary

The EUR/CHF currency pair has been showing a “contrarian” trend reversal tendency in addition to the trend repetition signal with a 24-hour-multiple time lag seen in most other currency pairs. EUR/CHF is not completely “efficient” from the point of view of basic two-point correlation analysis. Long term prospects of EUR/CHF are the subject of fundamental analysis and are outside the scope of this article. Cross-correlations with other markets are to be discussed in the up-coming articles. In this report we used data for the period from 00:00 2002-08-20 to 00:00 2008-02-01 (New York time).

CHF/JPY 2002-2008: Predictability Overview

The Swiss Franc/Japanese Yen in 2002-2008 has been showing a “contrarian” trend reversal tendency in addition to the trend repetition signal with a 24-hour-multiple time lag seen in most other currency pairs.

In this report we focus on the period from 00:00 2002-08-20 to 00:00 2008-02-01 (New York time). This is a pair of low yield currencies. The Bank of Japan held its discount rate at historic minima (hitting 0.1% in September 2001). Swiss National Bank’s three-month Libor rate target hit historic minimum in 2003-2004. On average for the period, the Swiss Franc enjoyed a higher yield.

CHF/JPY autocorrelation 1 hour time-lag bin

Fig.1: Autocorrelation of hourly logarithmic returns in CHF/JPY. The time lag is in “business time” (periods without update ticks are excluded). The red band shows the level of noise as iferred from martingale simulations (see text).

The basic autocorrelation

As before we employ autocorrelation as a straightforward, inter-disciplinary, non-proprietary technique to test market efficiency. In Fig.1 we look for features on the time scale of up to two days such as to suit the time scale of day trading or swing trading. The hatched red band shows the range of statistical noise (namely its expectation plus minus its RMS deviation). Statistical noise was obtained by simulating 20 independent time series of the length corresponding to that of the CHF/JPY series, each one constructed to reproduce the measured distribution of returns for CHF/JPY for the time period under study (including the fat tails!), but completely devoid of correlations ( martingale time series ). From these, the expectation and RMS or the autocorrelation amplitude in each time lag bin were calculated. The one-hour time lag “contrarian” feature (a significant anticorrelation) we saw on this plot in other currency pairs involving JPY ( GBP/JPY and AUD/JPY ) is also present in the CHF/JPY autocorrelation. The autocorrelation being an average of a product of hourly returns taken with a lag, this negativity means that we are way too frequently taking a product of opposite sign returns — or that the product of the opposite sign returns far outweighs that of the same sign returns. Because trend reversals on the time scale of about one hour happen either too often or are too lucrative, CHF/JPY, like GBP/JPY and AUD/JPY analyzed before, may well be the market where winning strategy requires being a clever contrarian. We increase the time lag bin to four hours in Fig. 2 to try and see if we can locate a trigger signal — something that could alert you to take a contrarian position with more confidence.

CHF/JPY autocorrelation 4 hour time-lag bin

Fig.2: CHF/JPY autocorrelation as in Fig.1, but with time lag bin increased to 4 hours.

In Fig.2, the time lag bin has been increased to 4 hours. This figure does not reveal any new reliable patterns, although one might argue there is a hint of a zigzag pattern with a period of about 2 weeks.

24-hour trading cycle.

CHF/JPY bullish and bearish autocorrelation

Fig.3: CHF/JPY bullish and bearish autocorrelations. Yellow: correlating only positive hourly returns. Blue: correlating only negative hourly returns.

In Fig.3 we construct autocorrelations of the subsamples of the full time series (the “bullish” and “bearish” ones) selected by taking only positive and negative returns respectively. The 24 hour cycle of bullish and bearish action is again clearly seen as the maxima of the correlation are located at multiples of the 24 hour lag: 24, 48, 72, 96, 120 hours and so on. Therefore, smart trend following means something more than following a trend that existed in the near past. It means following a trend that existed this time of the day yesterday, the day before yesterday, and so on — that gives you better than average chance of winning! Conversely, buying because the currency went up 12 hours ago (or selling because it went down 12 hours ago), all the rest being equal, is the least recommended strategy. (See why this cyclic correlation feature is not in itself a prediction mechanism.) Needless to say, this effect is not present in the simulated martingale data.

Note that whether this trend following pattern is equally strong in all time zones (at all times during the day) is a question that requires a separate study.

CHF/JPY bullish and bearish autocorrelation long range

Fig.4: CHF/JPY bullish and bearish autocorrelations. Axes and color codes as in the previous figure. Range expanded compared to the previous figure to show the characteristic time length of this market memory effect.

Similar patterns have been seen before with most other currency pairs in this series of predictability reviews. It is interesting to note that typically, such correlation has higher amplitude when “bearish” refers to the currency with higher interest rate. This has been seen with AUD/USD , AUD/JPY, USD/JPY, GBP/JPY, USD/CAD (although the interest rate differential has not been that high, it is in favor of USD), AUD/USD. While in the case of classic carry-trade currency pairs such as AUD/JPY this has been associated with the unwinding of the carry-trade, the underlying mechanism is likely to be similar for other currency pairs. The fact that one can read the sign of interest rate differential off the public forex quotes via basic correlation analysis is — should this interpretation prove correct — astonishing and indicates that despite large liquidity such interest rate differentials are not completely discounted by the markets and there remain profit opportunities for algorithmic trading.

Summary

As most other currency pairs analyzed, CHF/JPY is not completely “efficient” from the point of view of basic two-point correlation analysis. Long term prospects of CHF/JPY are the subject of fundamental analysis and are outside the scope of this article. Cross-correlations with other markets are to be discussed in the up-coming articles.