St Dev of a portfolio

Quick thing: in some examples (schweser), even assuming zero correlation between different managers (sub-portfolios), they calculate portfolio standard deviation as the weighted average of standard deviations but in other examples they do calculate the portfolio standard deviation as: = square root of sum of (weight of each portfolio times its st dev)^2 what should we do if we have to calculate it in the exam? I think the second is correct, and the first one is just an approximation, right? thx

the first one assumes correlation being one. the 2nd assumes correlation being zero.

thanks randOm one of the examples where st dev is just the weighted average (so correlation would be one) is an example where they calculate the st dev of a portfolio consisting of 2 corner portfolios. I guess this is wrong, isn´t it? I mean, 2 corner portfolios in the efficient frontier can´t have a correlation of 1, right? thx again

I have to review this, but I think the point about corner portfolios is that you can approximate the shape of the efficient frontier by just drawing a line between two corner portfolios (which are by definition on the efficient frontier). To do this, you would just do a weighted average of returns and a weighted average of volatilities. Remember that this is only an approximation, and on the exam it should only be used in a situation where you are using corner portfolios. Other times you should use the formula with (w1*SD1)^2 + (w2*SD2)^2 + 2*w1*w2*SD1*SD2*corr(1,2). The other time you can just do a regular weighted average is if you have two assets and one is the risk free asset. This is because there is 0 correlation in returns between a risk free and risky asset, and the risk free asset has no volatility of its own to contribute.