The original motivation for the technical, mostly correlation-based study of forex predictability, is “not supposed” to exist in liquid markets), may indeed take the front row sit at the LIBOR show. Perhaps, *predictability of risk* is a good phrase to discuss the subject matter at hand. Like the USD and EUR LIBOR reports, this document begins with historical LIBOR charts for the Japanese Yen, continues with volatility analysis, and culminates with correlations of logarithmic returns in JPY LIBOR.

### Executive summary

JPY LIBORs show great variation of correlation patterns with loan term. Correlations of short-term LIBORs look dominated by singular events; time-dependency analysis is required to tell you more. Autocorrelations of short term LIBOR exhibit the now familiar “bipolar disorder” pattern with the period of one (for s/n-o/n) or a few days (for 1-week LIBOR). The smooth wave-like patterns of intermediate term USD and EUR LIBORs, about 70 days in period, are not found in JPY. As the term duration increases, the main correlation pattern becomes that of positive correlation between different maturity terms as well as inside individual time series (autocorrelation). Longer term maturities are seen to strongly influence the future of the shorter terms in a positively correlated fashion.

During the period under consideration, BOJ raised the Basic Discount rate only twice: on July 14, 2006, from 0.10 to 0.40, and on February 21, 2007, from 0.40 to 0.75. Thus the interesting stuff begins in 2006. The “invisible hand” of the market jumps 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.

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

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

s/n-o/n | day | 5.3×10^{-2} |

week | day | 4.4×10^{-2} |

month | day | 3.5×10^{-2} |

6 months | day | 2.3×10^{-2} |

12 months | day | 1.4×10^{-2} |

Unlike USD and EUR, volatility of JPY LIBOR goes down for larger maturities.

The distributions of logarithmic returns on the day time scale look rather complex, possibly due to the fact that two histories with very different features are now mixed together: the pre-2006 and post-2006. 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 JPY 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 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* forecasting is straighforward for these duration terms: 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, usually justify no such strategy, and you will not find wide positive correlation peaks in forex. Trend following is not a viable strategy with s/n-o/n 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. 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. The cross-correlations of time series for different LIBOR terms show more positive correlation in the positive range of the time lag. In the figures, 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, longer term *leads* and shorter term *follows*.

#### 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