Correlation

A statistic describing the linear relationship between two series of returns. The coefficient runs from minus one, where the two have moved in exactly opposite proportion, through zero, where knowing one says nothing about the other, to plus one, where they have moved in exact proportion together. It is computed over a stated window, and the window is part of the answer rather than a detail of it.

Two choices decide what the number means. It is computed on returns, meaning changes, not on the price levels themselves, because two series that merely drift upward together will show a high coefficient on levels while sharing no relationship at all. And the length of the window sets the horizon being described: a coefficient over several years and a coefficient over the last month can carry opposite signs for the same two markets, and neither is wrong.

The practical warning has two parts. Correlation is not causation, and a coefficient is silent about which market moves first or why. More consequentially for risk, correlations are unstable, and they have historically converged towards one exactly when markets are falling together, which is when the diversification they were relied on to provide would have mattered most. Two positions in strongly correlated instruments are closer to one position of double the size than to two independent ones, and that is the arithmetic diversification depends on.