Pound Sterling (GBP) LIBOR Rates: Technical Predictability Overview

The original motivation for the technical, mostly correlation-based study of LIBORs was outlined in the USD LIBOR article. Like the USD, EUR and JPY LIBOR reports, this document begins with historical LIBOR charts for the Pound Sterling, continues with volatility analysis, and culminates with correlations of logarithmic returns in GBP LIBOR. You will see that predictable patterns in GBP LIBORs show great variation with loan term. Autocorrelations of short-term LIBORs look jittery on the next-day time scale. Autocorrelations of short term (s/n-o/n and 1-week) LIBOR exhibit the now familiar “bipolar disorder” pattern with the characteristic time period of no more than 2-3 days. The smooth wave-like patterns of intermediate term USD and EUR LIBORs, about 70 days in period, are also found in GBP. As the term duration increases, the main correlation pattern becomes that of predictive (non-zero time lag) positive correlation between different maturity terms as well as inside individual time series (autocorrelation).

LIBOR charts

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

Fig.1: Historical GBP 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 most striking feature is the high volatility of s/n-o/n and 1-week LIBOR rates in 2002 which gradually goes down. 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. Longer maturities develop patterns of their own while the shorter ones are dominated by the basic step-like pattern modulated by the short-range neurosis. 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 GBP LIBOR in 2002-2008, various maturities

durationtime scalevolatility (RMS)
s/n-o/nday7.8×10-2
weekday2.6×10-2
monthday5.8×10-2
3 monthsday3.8×10-2
6 monthsday6.6×10-2
12 monthsday7.1×10-2

Volatility of GBP LIBOR seems to have no easy pattern in its dependence on duration term.

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

Fig.2: Distributions of logarithmic returns in GBP 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 on the day time scale looks rather complex, reflecting the evolution of the LIBOR pattern with time — the jittery picture of 2002 will certainly result in a different logarithmic return distribution than the 2006 and 2007. The core distributions may be 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), but the long tails certainly do not belong to the same, if any, power law as the core distribution.

 

LIBOR autocorrelations

As with the Euro and the US Dollar LIBORs and with some of the most volatile forex exchange rates, the most prominent feature of the s/n-o/n and 1-week GBP 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.

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

Fig.3: Autocorrelation of logarithmic returns in the historical GBP 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 pairs of 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-week and longer term (but not 12-month) LIBOR autocorrelations are overall positive for the time lags of hunderds of days, with considerable evolution in shape. 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 LIBOR — forex exchange rates, on the contrary, generally justify no such strategy, and you will not find wide positive peaks in the forex return correlations.

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 GBP 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. 1-month, 3-month and 6-month figures show oscillations with what looks like 70 to 75 day period (counting business days only). Not sure what this has to do with periodicity of BOE meetings — but 70 days is twice the FOMC’s regular period. In fact, similar periodicity has been seen in the USD and EUR LIBOR autocorrelations for comparable maturities.

 

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. Here is the summary, followed by the data.

The covariance of different maturity terms (amplitude of the zero time-lag peak) is seen to go down as the difference in maturities grows; similar maturities are correlated tighter. The correlations become overall more positive between longer-term maturities.

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

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

 

Correlations between 1-week and longer term LIBOR rates

Correlation between logarithmic returns in 1-week and 1-month GBP LIBOR rates as a function of time lag, days Correlation between logarithmic returns in 1-week and 3-month GBP LIBOR rates as a function of time lag, days Correlation between logarithmic returns in 1-week and 6-month GBP LIBOR rates as a function of time lag, days Correlation between logarithmic returns in 1-week and 12-month GBP 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 GBP 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 pairs of uncorrelated time series.

 

Correlations between 1-month and longer term LIBOR rates

Correlation between logarithmic returns in 1-month and 3-month GBP LIBOR rates as a function of time lag, days Correlation between logarithmic returns in 1-month and 6-month GBP LIBOR rates as a function of time lag, days Correlation between logarithmic returns in 1-month and 12-month GBP 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 GBP 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 pairs of uncorrelated time series.

 

Correlations between 3-month and longer term LIBOR rates

Correlation between logarithmic returns in 3-month and 6-month GBP LIBOR rates as a function of time lag, days Correlation between logarithmic returns in 3-month and 12-month GBP 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 GBP 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 pairs of uncorrelated time series.