Forex correlation matrix

Correlation between 17 markets — 15 currency pairs, gold and bitcoin — over the last 250 trading days, and, next to it, the range each of those numbers has actually covered. The second half is the part nobody publishes, and it is the part that decides whether the first half means anything.

Pearson correlation of daily log returns. Positive means the two tend to move the same way, negative the opposite, and zero means the sample says nothing about one from the other.

Why a correlation without a window is not a measurement

The same two markets read +0.9 or +0.3 depending on how much history you use and when you stop, and a matrix that does not say which is a decoration rather than a number. That is not a small effect here: US30 against USD/CHF shows -0.23 over the headline window and has ranged from -0.37 to +0.43 across the 60-day windows in this sample.

So every cell above is paired with that range, measured by recomputing the same correlation over 60-day windows stepped through the whole history and taking the tenth to ninetieth percentile. A pair sitting at +0.85 that has never left +0.80 is a different fact from one that has been to +0.40, and the single figure hides which you are holding.

The least stable pairs

Ranked by how far the correlation has travelled, widest first. These are the cells where a hedge or a diversification argument built on the headline number is most likely to be surprised.

Flips is the share of windows that landed on the minority side of zero. It matters for the pairs near the middle: a mean of 0.02 can be a genuinely unrelated pair, or one that alternates between +0.5 and −0.5, and only this column separates them.

What this can and cannot tell you

It measures whether two markets moved together over a window. It does not say why, it does not say they will continue to, and it says nothing at all about direction — a pair of markets can be perfectly correlated and both be falling. The most common way this table gets misused is as a diversification proof: two instruments at +0.2 today are not thereby independent, as the range column keeps demonstrating.

Correlation is also not the whole of how two markets relate. Two currencies can both be lively and move together, leaving the cross between them asleep, or move apart and tear it open — a variance question rather than a correlation one, and not answered here.

The rest of the measurement: what each market does hour by hour, its average daily range by year, and how often price reaches a level once it is set.