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Statistics for finance · level 2

Correlation from covariance

Covariance has unreadable units. Divide by both standard deviations and it collapses into a number between −1 and 1 you can actually interpret.

Theory: Volatility, Correlation and Dependence

Worked example: Cov(x, y) = 24, σx = 6, σy = 8. Correlation?

covariance24
σx σy48
ρ0.5

Step by step

  1. 1

    Correlation is covariance, scaled

    ρ = Cov(x, y) / (σx σy)

  2. 2

    Denominator

    6 × 8 = 48

  3. 3

    Divide

    24 / 48 = 0.5

Cov(x, y) = 24, σx = 6, σy = 8. Correlation? = 0.5

The theory behind it

Intuition

Correlation is covariance normalised by both standard deviations, so it lives in [−1, 1] and is unit-free.

Common pitfalls

  • ×Reading correlation as causation.
  • ×Using correlation on non-linear relationships where it understates the link.

In the interview

Diversification and driver-analysis rounds.