This article begins a series of analysis reports investigating a degree of predictability in the LIBOR rates, a popular capital cost indicator. The analysis is based on historical LIBOR interest rate data released by the British Bankers Association. I continue with the same technique proved useful in the predictability analysis of forex exchange rates, as our interest in the interest rates in general is in part provoked by the results of the latter analysis, namely:

- sometimes, one forex exchage rate can “show the way” to a number of others, or in other words, foretell (in a probabilistic or statistical sense) their movement.
- when that happens, it is usually the exchange rate with a large interest rate differential showing the way to the ones with lower interest rate differentials.

Obviously, when exploring these “loopholes” or market inefficiencies for wealth generation, an algorithmic trader or a forex trading system (an automated decision making algorithm such as the one being built here on *Forex Automaton*™ site) must be mindful of the picture of LIBOR rates and its evolution, albeit in a somewhat different context than a long-term money manager. Being able to predict events, even in a weak statistical sense, is even better than merely following. Besides being useful via their implications for forex forecasting, LIBORs form an underlying indicator for derivatives of their own. LIBOR futures contracts and options on such contracts are traded on the CME. How does the predictability of LIBORs compare with that of currencies? Which one, LIBOR or forex, is more attractive to trade? Answering these questions, or providing a technical analysis framework to approach the answers, while leaving the fundamentals and event-driven trends aside, this series of articles about correlation features in LIBORs will serve as a useful compliment to our set of forex correlation analysis notes. I start this new series of articles with the all-important US Dollar LIBOR.

#### Executive Summary

The time series of US Dollar LIBORs is highly volatile; on the day scale, the distribution of “returns” (daily increments) is not only not lognormal but for some maturities not even power law. The main correlation pattern is positive correlation, between different terms as well as inside individual time series (autocorrelation). The heart-beat pattern of short-range LIBOR is replaced by longer-range waves and finally disappears in 12-month term data.

#### LIBOR charts

BBA tracks LIBORs for various loan durations (maturities). I focus on spot-next/overnight (s/n-o/n), 1 week, 1 month, 3 month, and 1 year maturities.

Comparing the histories of different LIBOR maturities in different panels of Fig.2, you see their regular and sharp pattern becoming progressively less sharp as the maturity increases, with the shortest, s/n-o/n LIBOR, having the sharpest structure. The origin of the negative spikes surrounding the zero time-lag peak is quite clearly visible: the history of LIBOR is full of false alarm events when the rate suddenly changes its course (typically, jumps up) only to correct itself completely the next day. The money markets jump the gun trying to anticipate the course of events almost regularly, to the extent this nervousness must represent a regular and significant arbitrage opportunity, if the market instruments tied to the LIBOR rates have the same features.

#### LIBOR volatilities

**Table 1:** Day-by-day volatilities (RMS) for the time series of logarithmic returns in USD LIBOR in 2002-2008.

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

s/n-o/n | day | 3.1×10^{-2} |

week | day | 1.4×10^{-2} |

month | day | 8.5×10^{-3} |

3 months | day | 8.4×10^{-3} |

12 months | day | 1.9×10^{-2} |

As you could have guessed from inspecting Fig.2, s/n-o/n LIBOR is more volatile than 1-week, whereas 12-month LIBOR is more volatile than 1-month and 3-month. Forex distributions on a shorter scale (one hour) look much less volatile than LIBOR, the “fat tails” in LIBOR distributions are truly amazing.

#### LIBOR autocorrelations

As was seen in Fig.1, the pediodic “heartbeat” pattern in the overnight LIBOR autocorrelation shows no signs of abaiting for the range of lags as long as 200 days. In Fig.4, you see that this “heartbeat” is unique to the overnight LIBOR, while some “gun-jumping” (short range negativeness) is also seen in 1 week LIBOR loan term data, but is gone in longer terms. Fig.1 and Fig.4 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, 1-month and 3-month LIBOR autocorrelations are overall positive, with a strong short-range peak. This is very different from forex exchange rates, and implies that *medium-range* LIBOR forecasting is straighforward for these duration terms: betting on the continuation of a trend, no matter whether the trend is up or down, is the winning strategy. In other words, trend following is possible with LIBOR — forex exchange rates, on the contrary, usually justify no such strategy, and you will not find wide positive correlation peaks in forex. Neither does the 12-month LIBOR where the wide peak around zero time lag is gone.

Federal Open Markets Committee (FOMC) holds its regular meetings every 7 weeks, that is 35 business days. One might expect that regularity to result in a feature of some kind corresponding to this time scale. The wavelength of the 1-month and 3-month LIBOR oscillations, see Fig.4, which is about 70 days, may be linked to that, being a multiple of 35.

#### Cross-correlations of LIBOR terms

Next, I am going to look at correlation between LIBOR rates of different maturities for various time lags.

Naturally, individual LIBOR maturities are generally positively correlated with one another. Speaking of forecasting, more often than not we see more positive correlation in the positive range of time lag. All correlated pairs are ordered so that shorter term is first, longer term second. The time lag being

t_{1}-t_{2},

the conclusion is that often, shorter term *follows* and longer term leads. 12-month term is seen to lead 1-week and 1-month; 3-month term is seen to lead s/n-o/n; so is 1-month.