Glossary term
Correlation
Definition
How two series tend to move together. Near 1 they travel as one. Near 0 they wander separately. In stress, many correlations rise — the grid goes one color.
How it works
Correlation measures how two return series tend to move together, on a scale from −1 to +1. The usual formula divides the covariance of the two series by the product of their standard deviations: ρ = cov(x, y) / (σx × σy). Near +1 the pair moves almost as one, near 0 their moves are unrelated, and near −1 they tend to move opposite ways.
It is a sample statistic: a number computed from whatever window of history was available, not a fixed fact about the world. Most history is calm, so the figure mostly describes ordinary weeks. In stress a single shared driver, such as forced selling or a repricing of risk, can dominate everything at once, and correlations that looked comfortable can rise together.
Worked example
Take a hypothetical two-asset book, 50% in each, with both assets at 20% annual volatility. Portfolio volatility is 20% × √(0.5² + 0.5² + 2 × 0.5 × 0.5 × ρ), which simplifies to 20% × √(0.5 + 0.5ρ).
At ρ = 0 that is 14.14%. At ρ = 0.5 it is 17.32%. At ρ = 0.95 it is 19.75%, and at ρ = 1 it is the full 20%. Nothing about either asset changed between those lines. Only the relationship moved, and nearly all of the benefit of combining them was lost.
Hypothetical, for education only. Not a recommendation and not a prediction.
Common mistake
The mistake is quoting a correlation measured in calm conditions as though it were a property of the pair. A coefficient of 0.35 over three quiet years can be accurate and still say almost nothing about the week the protection was wanted. A correlation should be quoted with its window, and the practical habit is to try to name the mechanism that makes it true. If you cannot, you are relying on a pattern.