Forex Correlation Matrix

The formula

r_t = price_t ÷ price_t−1 − 1
correlation = Σ(x−x̄)(y−ȳ) ÷ √( Σ(x−x̄)² · Σ(y−ȳ)² )

Standard Pearson correlation on daily percentage changes, not on price levels. That distinction matters: correlating raw prices produces impressively high numbers that mostly reflect shared trends rather than day-to-day co-movement, which is the thing that actually determines whether two open positions hurt you at the same moment.

Why this changes position sizing

The example of a trader having a long position in EUR/USD and GBP/USD (both with an equivalent 1% risk) and these being positively correlated at +0.90 provides a good example for how traders can take what would be a 2% dollar risk on their overall dollar exposure instead of taking separate 1% risks on the euro and pound. In addition, the large number of times when a trader has seen the loss from a broad dollar move wipe out many of the traders' other "diversified" trades simultaneously demonstrates the practical application of using the position size calculator to divide up a total risk allowance for a single trade among its multiple components when the components have high positive correlation.

Inverse correlation works similarly (and can be just as easily misinterpreted) but will show an inverse relationship of the two values. If you have a long position in EUR/USD and a long position in USD/CHF, you are essentially holding no position. You will still incur fees for both trades. A large, negative number in the matrix that represents the relationship between two positions held in the same direction means you may be hedging unintentionally.

The honest caveats

Correlation is backward looking and therefore likely to be both volatile and subject to some degree of instability. Moreover, correlation will tend to increase in value at the extremes (i.e., in times of extreme stress) precisely because that is when diversification has the least effect. Therefore, you should examine the same pair over different time frames (e.g., 30 day vs. one year) before making conclusions based upon a single correlation coefficient. In other words, if there are similarities across those time periods, then this may suggest that there exists a structural component to the relationship; for example, where the two sides of the same pair share the same side of the dollar. However, if they do not agree, then this may indicate that the correlation is simply transitory. The currency strength meter methodology further develops the above concept by separating pairs into their constituent parts (the two sides), and by including historical data in each side (as represented by the per-pair pages) from which all pair-wise correlations are calculated.