A correlation coefficient is a summary of one window of history. It is not a property of two instruments. Change the window and you change the number; change the sampling interval and you can change its sign.
This matters because correlation is usually consumed as though it were structural. A desk sees 0.82 between two currency pairs and concludes the pair is one position. Sometimes that is right. Often the 0.82 is an artefact of the window chosen.
What we compute, and over what
We compute Pearson correlation on log returns, at a fixed sampling interval, over an explicitly stated window. All three of those choices are visible wherever a number is shown, because a coefficient without them is not interpretable.
- Log returns, not prices. Correlating price levels finds trends, not relationships.
- A fixed interval. Mixing intervals across instruments with different session hours produces relationships that are partly an artefact of when each market was open.
- A stated window. A 20-day and a 200-day reading answer different questions. Neither is the correct one.
Where it breaks down
Three failure modes account for most of the damage:
- Regime change. A relationship that held through a low-volatility period frequently inverts when volatility expands. The historical coefficient is then actively misleading.
- Session mismatch. Two instruments that appear uncorrelated at a daily interval can be tightly linked during a single overlapping session.
- Common factor. Two instruments correlate because both respond to a third thing. When that third thing stops moving, the relationship evaporates without either instrument changing behaviour.
What we do about it
We report correlation alongside the stability of the relationship over sub-windows. A coefficient of 0.8 that has been between 0.7 and 0.9 all quarter is a different object from a coefficient of 0.8 that was −0.2 six weeks ago, and the interface distinguishes them.
Where a relationship has broken down, the reading says so rather than averaging the break away.
Correlation is not causation, and a stable correlation is not a guarantee of anything. It is one input for thinking about whether a book is as diversified as its instrument count suggests.