

Foreign Exchange correlations and inefficiency update, July 2012 
Written by Forex Automaton  
Sunday, 22 July 2012 13:29  
The first release of this study was published on this site in March 2012. Now, with four more data points and a new insight into the overall interpretation of the data, here is an update. As a reminder, I monitor three quantities:
CERPI and CERCSI are defined elsewhere on this site. The volatility measure has just been defined. CERPI measures the strength (by absolute value) of the 1hour lagged Pearson correlation coefficients among the individual time series (intermarket correlations) as well as inside each time series (autocorrelations). Benchmark level of CERPIDue to finite measurement accuracy, CERPI can and will be nonzero even for perfectly efficient markets. As a nonnegative quantity, CERPI is an average value statistic of an asymmetric distribution, describing an absolute value of the correlation coefficient corresponding to the time lag of one hour. The correlation coefficient is a random quantity which is equally likely to take both positive and negative values in the hypothetical case of efficient markets. The distribution of its absolute value can be approximately described as the right half of the typical bellshaped Gaussian distribution whose sigma equals the measurement accuracy for a typical onehour lag correlation, with zero being the left margin of the distribution. As figures in the Correlation Reports section indicate, this measurement accuracy appears to be about 0.05 (hourly data, a month of observation). If we take a Gaussian with sigma s, mean 0 and cut it in two, leaving only the right part and renormalizing it, the resulting distribution will have mean of s (2/3.1415...)^{1/2} or about 0.8s. This means that the value of CERPI to expect from the perfectly efficient markets would be around 0.04. 1.1 1.2 1.3 The time evolution plots of CERPI, CERCSI and volatility are shown in Fig.1. Gray line in Fig.1.1 underscores the nontrivial information in CERPI: had the markets been efficient, the data would have been centered around the gray line. The data are considerably higher on average, arguably with a slight trend towards greater efficiency (lower CERPI) as time goes on. Fig.1.2 indicates that in the past three months the markets have been moving into the zone of higher absolute value correlation, usually associated with periods of market panics. (Naturally, various pairs of market instruments are either positively or negatively correlated. By high "absolute value" correlation I mean that correlations in general grow in absolute value: the positive ones get more positive while the negative ones get more negative). Portfolio diversification breaks down as the universe of financial instruments degenerates into risky assets and safe haven ones. This degeneration, even though it may be linked with high volatility via investor psychology and via the mechanics of the overleveraged markets, does not follow from a rise in volatility mathematically, and represents an independent aspect in the quantitative description of the panic phenomenon. Interestingly, the present values of CERCSI, historically high, are accompanied by moderate volatility. 