# standard deviation of the portfolio

I’ve seen simple weighted avarage as below: SD§ = W(a) * SD(a) + W(b) * SD(b) variance § = SQ (W(a)) * SQ (SD (a)) + SQ (W(b)) * SQ (SD (b)) + 2* W(a)* SD (a) *W(b)* SD (b)* correlation (a,b) are they both correct or did i miss something?

I THINK first one is for corner portfolio stuff, don’t need to square and all that jazz, just simple weighted average.

variance § = w(a)^2 * sd(a)^2 + w(b)^2 * sd(b)^2 + 2*w(a)*w(b)*sd(a)*sd(b)*correlation(a,b) sd dev § = sqrt (Variance §) when calculating on a = asset b= currency, remove the weights from the forumla and calculate.

yeah corner portfolio uses linear approximation which throws me off big time I go with this rule: If they give you correlation - use the real equation If they do not - use linear approximation

Bib Babbu, That’s correct. but how does this one differ from the simple weighted average of standard deviations? variance § = w(a)^2 * sd(a)^2 + w(b)^2 * sd(b)^2 + 2*w(a)*w(b)*sd(a)*sd(b)*correlation(a,b)

^^ i think jscott has it right… thats what i have been following and it seems to work

Linear Approximation = weighted average?

Good question, beyond my understanging at this point. I wonder if the weighted averages is just an approximation you use to calculate in a corner portfolio question.

to sum up: Linear Approximation = weighted average; variance § = w(a)^2 * sd(a)^2 + w(b)^2 * sd(b)^2 + 2*w(a)*w(b)*sd(a)*sd(b)*correlation(a,b) Currency/ Asset: variance § = sd(a)^2 + sd©^2 + 2 * sd(a)*sd©*correlation(a,c) does it look right this time?

Yes thats correct So no correlation W(a)Std(a) + W(b)Std(b) This is the maximum standard deviation possible when you combine these portfolios

this is a spot to CFAI could be tricky on in corner portfolios----ie. watch out for correlation matrix

Here’s what Schweser says, Any time you estimate a value as a weighted average you assume linear relationship. By estimating in this way we assume no diversification benefits, the estimated st dev actually represents the maximum st dev when the portfolios are combined in certain weighs. So I guess there’s a conservatism assumption built into the process.

Eyes to brain - URGENT. Word “currency” has appeared, shut down immediately!!!

My god, I would assume they would give us the easy way out on this one. That thing has been tested at L1 and L2. But, it is CFAI so be on those toes.