How do I interpret the covariance between two assets?

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AcadiFi · Accepted Answer

Covariance measures how two variables move together. Formally, Cov(X,Y) = E[(X - μₓ)(Y - μᵧ)]. A positive covariance means the two assets tend to move in the same direction, negative means opposite, and zero means linearly unrelated.

The problem with raw covariance is scale dependence. Your value of 0.00082 is in units of (decimal return)² if your returns are decimals, or in units of (percent return)² (so 0.82%²) if you worked in percents. It's hard to interpret magnitude directly. That's why we typically convert to correlation:

ρ = Cov(X,Y) / (σₓ · σᵧ)

If Greenfield has σ = 3.2% monthly and Hawthorne has σ = 2.1%, then correlation = 0.00082 / (0.032 × 0.021) = 1.22. That's impossible (correlation is bounded by ±1), so the 0.00082 must be in units that yield a reasonable ρ. If instead Cov = 0.00000082 in decimal squared terms (equivalently 0.00082% in squared percents), then ρ = 0.00082% / (3.2% × 2.1%) = 0.12, a mild positive correlation.

For portfolio risk: σₚ² = w₁²σ₁² + w₂²σ₂² + 2w₁w₂Cov(X,Y). Even small positive covariances compound when many assets are combined. That's why diversification becomes less effective as correlations rise during market stress. CFA candidates should always translate covariance to correlation for interpretation and keep units consistent between inputs.

How do I interpret the covariance between two assets?

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