LIBOR patterns: the story continues with CME:EM futures

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Written by Forex Automaton   
Thursday, 03 September 2009 11:49

With the remarkable correlation patterns seen in the logarithmic return autocorrelation data for LIBOR, the question of practical importance is to see how much of the pattern survives in the freely traded instruments related to the interest rates. This question will be addressed in several installments. I begin with Eurodollar futures traded on Chicago Merchantile Exchange (CME). This is the first article in the sequel series on the subject.

Here are the technical details. The symbol CME:EM denotes a 1-month Eurodollar futures contract traded on CME by open outcry and electronically on Globex. The underlying instrument of the contract is the Eurodollar Time Deposit having a principal value of $3,000,000 with a one-month maturity. The word Eurodollar refers to US Dollars held on deposits outside the US. This word is much older than the single European currency and has nothing to do with it. The contract is quoted in the so-called IMM index points (IMM stands for International Monetary Market, a division of CME) or 100 minus the depost rate on an annual basis over a 360 day year. Expiring contracts are cash-settled to BBA's 1-month US Dollar LIBOR on the last trading day of the contract.

For purposes of technical analysis, it is necessary to create a long-term price series out of the individual futures contracts. In this study, back-adjusted data are used. Back-adjustment refers to the process whereby different segments of the price series, representing the individual contracts, are spliced together. In the process, the prices in the segments are shifted by the amount of the roll-over differential (the difference in the prices of the contracts being rolled-over one into another on the day of the roll-over). The resulting time series used in the analysis is shown in Fig.1.1.

History of the 1-month LIBOR CME contract price since 1995, day 1.1 History of the 1-month LIBOR CME contract volume since 1995, day 1.2 History of the 1-month LIBOR CME contract open interest since 1995, day 1.3

Fig.1:History of the 1-month LIBOR CME (CME:EM) contract data since 1995, day scale. 1.1: price, back-adjusted data; 1.2: volume; 1.3: open interest. Volume and open interest are shown in number of contracts. Time axis is labeled in MM-YY format.

 

Year 2004, when the cyclic rise in the US interest rates began, marks the top in terms of Eurodollar futures volume traded, exceeding the surrounding "grass" in the plots by order of magnitude. With up to 100,000 contracts traded daily in 2004, the LIBOR futures market at CME could well be the most liquid market in the world at that time.

History of CME:EM autocorrelation peak structure, since 1995, day scale 2.1 History of CME:EM autocorrelation peak structure, since 1995, day scale, zoomed 2.2

Fig.2: History of CME:EM autocorrelation peak structure since 1993, day scale. Time bin is 1/3 of a year wide. The autocorrelation is constructed for logarithmic returns in the daily close price. The peak structure is represented by three correlation values: the one for the zero lag (essentially a volatility measure) downscaled by 10 for easier visual comparison, the one at the one day lag and the one at the two day lag. Time axis is labeled in MM-YY format and spans the interval from January 1, 1995 to September 1, 2009. 2.2 is the same figure zoomed to enable visual inspection of the low volatility periods.

Fig.2 shows the evolution of the autocorrelation structure in the vicinity of zero time lag, representing the correlation structure as a triplet of correlation values: those at zero, one and two day lags. The increased volatility shows up as the increase in the magnitude of all these values, with variance (a measure of volatility) being fairly well represented by the magnitude of the zero time lag value.

Correlations with non-zero time lags are of particular importance for the purpose of algorithmic trading system development, since their presence indicates predictability of one time series on the basis of itself.

 

Autocorrelation of logarithmic returns in CME:EM,   day scale, from January 1, 1995 to September 1, 2007. 3.1 Autocorrelation of logarithmic returns in CME:EM,  day scale, from  September 1, 2007 to September 1, 2009. 3.2 Autocorrelation of logarithmic returns in CME:EM, comparison of the two periods. 3.3

Fig.3: Autocorrelation of logarithmic returns in CME:EM (futures on 1-month LIBOR) shown against the backdrop of statistical noise (red). 3.1: the measurement time range covers the relatively low volatility period, from January 1, 1995 through September 1, 2007. 3.2: same for the crisis phase, from September 1 onwards. These periods are denoted A and B as shown in Fig.2. The noise is obtained from martingale simulations based on the recorded volatilities of CME:EM for the respective periods. 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 of the same average volatility. 3.3: comparison of period A and period B autocorrelations, re-normalized to the unit variance for apples-to-apples comparison of non-zero lag features.

In Fig.3, the correlation pattern is investigated with the focus on the rest of the time lags (in addition to the three shown in Fig.2) and on the issue of statistical significance. The latter issue is addressed in the usual way by Monte-Carlo simulating independent time series with the CME:EM volatility of the period (A or B), from which the expectation value and the RMS of the correlation value as-if-the-market-were-efficient are inferred.

The quality of the analysis depends on how the non-stationarity of the time series is being treated. Fig.2 shows how we split the time series into the fragments A and B. What is conventionally regarded as the present financial crisis, is mostly contained in fragment B, of much higher volatility overall. Considering each piece as stationary is much better than considering the entire time series as stationary.

Significant (several RMS) deviations of the measured values from the Monte Carlo reference form the basis for interpretation, the goal being to find the better-than-casino aspects of the markets on the time scale of observation, days in our case.

To do justice to the data, the patterns in period B are so strongly visible that their non-randomness is evident even without noise-reference simulations. The patterns look like a replay of the LIBOR theme seen in an earlier analysis of spot-next/overnight (s/n-o/n) LIBOR, and Fig.3 should be compared to Fig.1 of that report.

In the s/n-/o/n US LIBOR autocorrelation (Fig.1 of that older report), one sees an oscillation with a period of about 10 days, clearly pronounced for the 20 periods shown in the figure and likely more. The autocorrelation of an oscillating time series is in itself an autocorrelation. This does not imply that all there is to the LIBOR price series is osicllation, but rather, that the oscillation is the most permanent, stable, regular feature on top of possibly many others, accompanied by fair amount of random behaviour.

In Fig.3.2, there are arguably 19-20 periods fitting the space of lags from 0 to 100, making the oscillation period of about 5 -- twice as short as in s/n-o/n LIBOR. Being twice as short, it's concievale that the CME:EM responds to the stimuli sent by the spot LIBOR, adding a higher frequency in the process.

Meanwhile, the autocorrelation for the underlying instrument itself, the 1-month USD LIBOR, looks quite different -- see Fig.4 following the link. The fact that oscillations of the futures look much closer to the spot/next LIBOR than to the underlying 1-month LIBOR looks surprising and possibly has an entirely psychological explanation.

Finally, the autocorrelation for period A probably can not be called entirely random as the traces of periodicity can be discerned there as well, but they are not nearly so strong as those in period B. Needless to say, patterns like Fig.3.2, manifested for a time period of two years, present a wealth-generating opportunity to the algorithmic trader equipped with tools to discern them on time and to synchronise their trading with the phase of the oscillation. Whether this should be called an opportunity of lifetime or of a much shorted time span remains to be seen -- Fig.3.1 with its faint traces of similar regularity lending hope that similar opportunities may present themselves more frequently.

To be continued -- with a study of intermarket correlations between LIBOR and its futures as well as volume and open interest.

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Last Updated ( Monday, 04 January 2010 12:29 )