Kaplan book 2 exam 2 AM question 6 part b

Hello, I am using Kaplan’s CFA Level 3 mock exams. Is the answer for the CFA Level 3 Kaplan mock exam book 2 - exam 2 AM question 6 part B incorrect? It states that standard deviation of the portfolio equals 0.764*(5.8%) + 0.236*(7.8%) = 6.27%?

The formula for standard deviation of a portfolio is square root of [(weight 1^2)*(variance of portfolio 1) + (weight 2^2)*(variance of portfolio 2) + 2*(weight 1)*(weight 2)*Cov(portfolio 1 and portfolio 2)]. Why are the weights and standard deviations not squared per the equation in my last sentence? I agree with the calculation for portfolio weights given by Kaplan, but not the standard deviation of the portfolio calculation.

Thank you.

I believe the question you’re referencing is related to corner portfolios. Whenever you are deducing the standard deviation of a mix of corner portfolios, you essentially are assuming:

-that the two corner portfolio’s are not at all correlated (i.e. zero correlation)

-that the underlying portfolios are well diversified in their own right, in that they are each allocated across several asset classes underlying the corner portfolio composition

-an overall conservative estimate of standard deviation in simply taking the weighted average of the two corners; will overstate standard deviation, but that’s ok as we’d rather err on the side of caution rather than underestimate potential risk.

Trust me, i’ve ran into the same mental block you’re encountering.

Thank you govt_cheese!