Patterns of financial crisis: EUR/USD in 2007-2008.

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Written by Forex Automaton   
Monday, 19 January 2009 16:51

I continue the "topical" theme of financial crisis, namely how it's seen through the optics of correlation analysis. With the data so far it looks like the crisis does have a unique correlation aspect to it: the increased volatility of the "impact phase" is not just large, but seems to be accompanied by a particular (non-random) correlation structure. Rather than being a "random walk" with a long step, it's a walk where each step (abnormally large indeed) is slightly more likely to be in the direction opposite to that of the previous step. As before, I use logarithmic returns on the hour time scale.

Evolution of EUR/USD exchange rate during the financial crisis, hour.

Fig.1:EUR/USD during the financial crisis, hour time scale. The time axis is labeled in MM-YY format and spans the interval from August 2, 2007 through December 31, 2008.

I define the visible phase of the present financial crisis to begin on August 16, 2007, the day of Countrywide Financial near-bankruptcy event, followed by an extraordinary half-percent Fed discount rate cut next day. This study covers 74 weeks from August 2, 2007 through December 31, 2008. The sub-range of extreme volatility (as will be seen in Fig.4) can be roughly defined as the last 18 weeks of this 74-week range. In this study, I only look at trading activity taking place from 1am to 1pm New York time, since the experience shows it to be the richest in non-trivial correlations.

EUR/USD volatility change during the financial crisis, hour.

Fig.2:The histogram of logarithmic returns in EUR/USD on the hour time scale demonstrates volatility change in the course of the financial crisis.

While the change in the volatility between the beginning of the crisis and its "phase of impact" is undeniable, single-point distributions like Fig.2 do not tell the whole story. These distributions could belong to a random walk or to a more complex pattern where prehistory matters.

Autocorrelation of logarithmic returns in EUR/USD,  European trading hours, hour scale, from August 2, 2007 through August 27, 2008. Autocorrelation of logarithmic returns in EUR/USD,  European trading hours, hour scale, from August 28, 2008 through December 31, 2008.

Fig.3: Autocorrelation of logarithmic returns in EUR/USD for the European (Eurasian) trading shown against the backdrop of statistical noise (red). Top panel: the measurement time range is for the relatively low volatility phase of the crisis, from August 2, 2007 through August 27, 2008. Bottom panel: same for the high volatility phase, from August 28, 2008 through the end of 2008. The noise is obtained from martingale simulations based on the recorded volatilities of EUR/USD in the trading hours under study for the period. 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. From top to bottom, the shape of the autocorrelation in the vicinity of the zero-time lag peak undergoes a transformation.

The difference is not just that the volatility got high in the impact phase of the crisis (making the Fig.2 distribution wider and Fig.3 -- higher). The difference is the appearance of a correlation pattern new to EUR/USD -- the pattern I call "bipolar disorder". This pattern has been seen before in forex exchange rates with high interest rate differential at stake, and also in LIBOR time series analyses. The "bipolar disorder" feature, a tendency to form quickly alternating rises and falls on next-hour time scale, more pronounced than in a fully unpredictable time series of the same volatility, shows up as negative deeps surrounding the zero-time lag peak (just recall that the product of returns having the opposite sign is negative). These have significance of over two standard deviations in the time-integrated correlation of Fig.3, bottom panel. The practical implication of a feature like this is simple: since any movement is likely to be followed by the movement in the opposite direction, it is hard to make money on trend following. Rephrasing the Wall Street adage, bulls get slaughtered, bears get slaughtered, pigs get slaughtered, contrarians (and brokers) make money.

Evolution of EUR/USD autocorrelation peak stucture during the financial crisis, hour.

Fig.4: Evolution of EUR/USD autocorrelation peak structure during the financial crisis, hour time scale. Time bin is two weeks wide. 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 one hour lag (just discussed) and the one at two hour lag. Time axis is labeled in MM-YY format and spans the interval from August 2, 2007 through December 31, 2008. Only trading hours from 1am to 1pm New York time (European trading hours), usually rich in non-trivial correlations, are included.

The time period of dramatically higher volatility covers the last 9 bins in Fig.4, which contain 18 weeks, from August 28, 2008 through December 31, 2008 (naturally, the choice of dates is to a certain extent forced by the bin width). The first two weeks of December, marked by dramatic revenge of Euro (see historical EUR/USD chart for December 2008) are very remarkable in Fig.4 as well (second bin from the right): this is the only bin in the high volatility phase with positive 1-hour lag and 2-hour lag autocorrelation values -- so strong and "deterministic" was the December offensive of the European currency. No doubt this signal, whose impact is included in Fig.3, bottom panel, takes a lot away from the "bipolar disorder" signature (of Fig.3, bottom panel), making it only marginally statistically significant at two standard deviations. Thus, pure "bipolar disorder" is the correlation footprint of the US Dollar strength which accompanied the volatile phase in 2008. Fundamentals aside, isn't it justifiable to call this USD strength pathological?

Taking this insight back to the EUR/JPY analysis, the bin starting October 23, 2008 and ending November 6 similarly sticks out in Fig.4 of that post. Similarly, an upward correction in the EUR/JPY took place during that time, although it's by no means as significant as that in EUR/USD in December.

The data used are from the period 2002-08-02 00:00:00 to 2009-01-01 00:00:00, New York time.

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Last Updated ( Monday, 04 January 2010 12:42 )