Patterns of financial crisis: GBP/USD, Footsie and the Dow

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Written by Mikhail Kopytine   
Tuesday, 24 February 2009 17:48

It just occured to me that a better way to look at a correlation between stock markets and forex (as always, in search for leading indicators) is to construct a forex-like ratio of two stock indexes and correlate that with the corresponding ratio of the nation's currencies. Therefore today I am studying correlations between FTSE-100/DJIA (the ratio of Britain's and US' blue chip indexes, Footsie and the Dow) and GBP/USD.

With the ratios costructed this way (symmetrically), one would naively expect a negative correlation: the value of dividend-generating assets such as stocks is negatively correlated with the cost of money, even without stock market bubbles in the picture, but especially when such bubbles are part of the picture. As before, I work with logarithmic returns, therefore it's irrelevant in what units the quantities are expressed (that is how these indexes are defined and what absolute magnitude they typically assume).

 

Evolution of GBP/USD from August 2007 through January 2009, day Evolution of FTSE/DJIA from August 2007 through January 2009, day

Fig.1:Top: GBP/USD chart, day scale. Bottom: FTSE/DJIA (day close) evolution. Time axis is labeled in MM-YY format and spans the interval from August 2, 2007 to February 12, 2009.

Time evolution of the structure of the GBP/USD and FTSE/DJIA correlation peak, day scale, from August 2, 2007 to February 12, 2009. Negative lags. Time evolution of the structure of the GBP/USD and FTSE/DJIA correlation peak, day scale, from August 2, 2007 to February 12, 2009. Positive lags.

Fig.2: Evolution of the correlation between GBP/USD and FTSE/DJIA  during the financial crisis, day time scale. The peak structure is represented by three correlation values: the one for the zero lag (essentially a volatility measure), the one at (plus or minus) one day lag and the one at (plus or minus) two day lag. Negative lags are in the top panel, positive lags -- in the bottom panel. Time axis is labeled in MM-YY format and spans the interval from August 2, 2007 through February 12, 2009, with two-week wide bins.

As before, 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 80 weeks from August 2, 2007 through February 12, 2009. Fig.2 shows the time evolution of the correlation peak by plotting the correlation values for the negative and positive lags in separate panels.

The time lag is defined as

td = t1 - t2,

where index "1" denotes GBP/USD and index "2" denotes FTSE/DJIA. Therefore, positive correlation value at negative lags means that movements of the same direction in GBP/USD and FTSE/DJIA happen at an earlier time in GBP/USD, or GBP/USD is a leading indicator for FTSE/DJIA. Such was the situation during the extreme volatility period in Fall 2008, as seen in the figures. This is the usual paradox since the same figures show FTSE/DJIA to be negatively correlated with GBP/USD, at least during the highest volatility pediod, as one would naively expect based on the cost of money argument above: nation's stock market and nation's money are negatively correlated. Apparently trading would have been "too easy" had the predictive correlation maintained the same sign for a considerable range of time lags. The actual pattern falls into the same category of bipolar-disorder phenomena explored in the forex reports studying the present crisis: see for example EUR/USD.  The -1 day lag correlation magnitude is truly huge with relation to the variance (0-day lag labeled "same day"). Efficient market hypothesis, on the contrary, prescribes no pre-history dependence in liquid markets and thus, only zero correlation values at non-zero time lags.

Note that, as this series of "patterns of crisis" reports goes on, I've reduced references to martingale simulations as a means of establishing the statistical significance of non-trivial features like the one in Fig.2, top panel -- simply because with so much evidence no special procedures are needed to make it clear that these patterns are not random coincidences.

Back to Fig.2, bottom panel -- a negative correlation value at positive lags means that movements of the opposite direction in GBP/USD and FTSE/DJIA happen at an earlier time in FTSE/DJIA, or FTSE/DJIA is a leading indicator for USD/GBP (which is line with the naive cost of capital argument, except that it is a fall in the stock market that begets expectations of a fall in the value of the currency and not the other way round).

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Last Updated ( Monday, 04 January 2010 12:39 )
 

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