Omitting the second covariance cross term

Expand the return deviation

Squaring wA(RA−μA)+wB(RB−μB) produces two own squared terms and twice the product of deviations. Taking expectations makes that product covariance. Symmetry does not mean one of the two products can be dropped.

Quantify the original missing term

In the default pair, one covariance product is 0.4×0.6×0.006=0.00144. Adding it only once gives variance 0.01144 rather than 0.01288. Taking a square root afterward cannot repair the omission.

Read the same fact in matrix form

Preserve negative covariance too

The factor two applies whether covariance is positive or negative. Under negative covariance, dropping a cross term understates the offset rather than giving the same direction of error as the positive example. Check the identity before relying on a sign-based shortcut.