weighted standard deviation from multiple means

Question

I have some stock return averages, and their standard deviations:

Stock A: 10% mean, 16% SD

Stock B: 8% mean, 14% SD

Stock C: 5% mean, 7% SD

Now, I want to construct a portfolio from these three stocks with different weights, and from that I get a weighted average:

(10 * 40%) + (8% * 10%) + (5% * 50%) = 7.3% weighted mean

My question is: is there a way I get a weighted standard deviation for this new weighted mean?

Answer 1

The combined SDs (square root of the average sum of the variances) without weighting is 12.9%. If you stir in weighting to the sum of the variances and take the square root, then this comes out to be 12.1%.