Correlation
Quantitative Finance glossary · Probability, Statistics & Linear Algebra
Definition
Dimensionless linear-comovement measure ρ_X,Y = (Cov(X,Y))/(σ_X σ_Y) in [-1, +1] — the normalised covariance. Captures only linear dependence; ρ = 0 does not imply independence (e.g. Y = X^2 with X symmetric). Sample correlation has standard error ≈ 1/√(n) for iid Gaussian data — far too noisy to invert into a stable covariance matrix without shrinkage (Ledoit-Wolf) or factor-structure imposition. Tail correlation rises sharply in crises (correlation breakdown).
Correlation in plain English
Correlation is a single number between -1 and +1 that answers 'when one thing goes up, does the other tend to go up too?' — plus one means they march in lockstep, minus one means they move in perfect opposition, and zero means no straight-line link. Here's the catch students miss: zero correlation does NOT mean 'unrelated.' Two things can be tightly connected in a curved way (imagine one variable equals the square of another) yet show zero correlation, because the measure only spots *straight-line* relationships. Two more warnings the pros live by: correlation estimated from limited data is noisy and shaky, and — dangerously — correlations tend to spike toward one during market crashes, so investments that looked nicely spread out can all sink together exactly when you needed them not to.
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