Correlation and covariance

No asset trades in isolation. Correlation measures how two return series move together, on a scale from −1 to +1.

• +1 — they move in lockstep.
• 0 — no linear relationship.
• −1 — they move exactly opposite.

Covariance is the unscaled cousin of correlation; correlation is just covariance divided by the two standard deviations, which puts it on the clean −1 to +1 scale.

Why it is the heart of diversification

Combining assets that are not perfectly correlated reduces portfolio volatility without necessarily reducing return — the core insight of modern portfolio theory. Two risky assets with low correlation can form a portfolio less risky than either alone.

The traps

• Correlation is not causation. Two series can correlate because both respond to a third hidden driver, or by pure chance over a short sample.
• Correlation only captures the linear part. Two variables can be strongly related and yet show near-zero correlation if the relationship is curved.
• Correlations break exactly when you need them. In a crisis, assets that were uncorrelated for years suddenly all fall together — diversification evaporates at the worst moment. This is the single most dangerous assumption in risk modelling.

A correlation matrix estimated in calm markets is a fair-weather friend. Treat it as a tendency, not a guarantee.