Variance of a two-stock portfolio when the stocks are linked

Question

You hold one share each of two stocks. Their returns have variances $\mathrm{Var}(A) = 9$ and $\mathrm{Var}(B) = 16$ , and their covariance is $\mathrm{Cov}(A, B) = 6$ . The combined return is

$P = A + B.$

What is the variance of the combined return?

Accepted Answer

When two quantities are linked, the spread of their sum is not just the sum of the two variances; you also have to account for how they move together. The full rule is \mathrm{Var}(A + B) = \mathrm{Var}(A) + \mathrm{Var}(B) + 2\,\mathrm{Cov}(A, B). In words: add the two variances, then add twice the covariance. The extra covariance term appears because when both tend to be high at the same time, their swings reinforce each other and the total swings more. Apply it. \mathrm{Var}(P) = 9 + 16 + 2(6) = 25 + 12 = 37. The standard deviation is \sqrt{37} \approx 6.08. It is worth seeing what the lin…

Variance of a two-stock portfolio when the stocks are linked

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