“An investment operation is one which, upon thorough analysis promises safety of principal and an adequate return. Operations not meeting these requirements are speculative.” Apparently for Graham and Dodd, the term “speculation” has no positive connotations.

## 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

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

duration | time scale | volatility (RMS) |
---|---|---|

s/n-o/n | day | 7.3×10^{-2} |

week | day | 4.8×10^{-2} |

month | day | 2.6×10^{-2} |

3 months | day | 2.2×10^{-2} |

6 months | day | 2.2×10^{-2} |

12 months | day | 2.4×10^{-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.

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.

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.

duration | s/n-o/n | 1-week | 1-month | 3-month | 6-month | 12-month |
---|---|---|---|---|---|---|

s/n-o/n | 1 | 0.73 | 0.51 | 0.32 | 0.25 | 0.17 |

1-week | 1 | 0.62 | 0.46 | 0.35 | 0.28 | |

1-month | 1 | 0.77 | 0.66 | 0.51 | ||

3-month | 1 | 0.85 | 0.66 | |||

6-month | 1 | 0.85 | ||||

12-month | 1 |

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

#### Correlations between 1-week and longer term LIBOR rates

#### Correlations between 1-month and longer term LIBOR rates

#### Correlations between 3-month and longer term LIBOR rates

## 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

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

duration | time scale | volatility (RMS) |
---|---|---|

s/n-o/n | day | 7.8×10^{-2} |

week | day | 2.6×10^{-2} |

month | day | 5.8×10^{-2} |

3 months | day | 3.8×10^{-2} |

6 months | day | 6.6×10^{-2} |

12 months | day | 7.1×10^{-2} |

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

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.

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

#### Correlations between 1-week and longer term LIBOR rates

#### Correlations between 1-month and longer term LIBOR rates

#### Correlations between 3-month and longer term LIBOR rates