The standard deviation of a portfolio is always the weighted average of the standard deviations of assets in the portfolio.

Question

Quizplus · Accepted Answer

The standard deviation of a portfolio is not always the weighted average of the standard deviations of assets in the portfolio. It also depends on the correlation between assets in the portfolio. The formula for calculating the standard deviation of a portfolio is: 
portfolio standard deviation = sqrt(W1^2 x σ1^2 + W2^2 x σ2^2 + 2 x W1 x W2 x σ1 x σ2 x ρ1,2) 
where W1 and W2 are the weights of asset 1 and asset 2 in the portfolio, σ1 and σ2 are the standard deviations of asset 1 and asset 2, and ρ1,2 is the correlation coefficient between asset 1 and asset 2.

The Standard Deviation of a Portfolio Is Always the Weighted