Turning a covariance into a correlation for two stocks

Question

Two stocks have daily returns X and Y with covariance 12. Stock X has variance 16 (standard deviation 4) and stock Y has variance 25 (standard deviation 5). What is the correlation between the two returns?

Accepted Answer

Covariance tells you the direction of the link, but its size is hard to judge because it depends on the units. Correlation fixes that by dividing out both spreads, producing a clean number that always sits between -1 and +1: \rho = \frac{\mathrm{Cov}(X, Y)}{\mathrm{SD}(X)\,\mathrm{SD}(Y)}. In words: take the covariance and rescale it by the two standard deviations, which strips away the units and leaves a pure strength-of-link number. Get the standard deviations. They are the square roots of the variances: \mathrm{SD}(X) = \sqrt{16} = 4, \qquad \mathrm{SD}(Y) = \sqrt{25} = 5. Divide. \rho = \…

Turning a covariance into a correlation for two stocks

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