# Approximate standard deviation of portfolio

Not sure if I am missing somthing uber-obvious here so hope somone can help. Approximate standard deviation of portfolio for a corner portfolio. Simply the weighted sum of the standard deviations (est. assuming linear relationship as no correlation ir max stdev) However in the Core Satellite approach example, to calculate the portfolio active risk they use the traditional formula. ie = sqrt(variance of a* weight of a^2 + variance of b* weight of b^2) Pls can someone help me out with what I am missing here. thanks

I’d be interested in knowing the why behind this too. Using just the portfolio weights for the standard deviation you end up with the maximum standard deviation the combined portfolios could possibly have. Why do we do it this way? Why do we care? I’m clueless. (However, it’s easier mathematically speaking.)

for corner portfolios they assume there is no correlation between them.

yep agree, which will/ should be the same assumption with the core satellite approach. I was just wondering why they use sqrt of the variance and weight squared for core satellite vs just the weighted sum of the stdev’s for the corner portfolio’s?

To the contrary, they are assuming that there are no diversification benefits from holding two (or more) asset classes. (corr = 1) stdev = (0.6)*(0.12) + (0.4)*(0.1) = 11.2% stdev = [(0.6^2)*(0.12^2) + (0.4^2)*(0.10^2) + 2*0.6*0.4*0.12*0.10*1] ^ (1/2) = 11.2% So, this assumption actually give you a more conservative (higher) portfolio stdev.

Very nice - I shld have realized Thanks again

Ok, so to summarize: With core-satellite approach, correlation between portfolios is assumed to be 0? With corner portfolios, correlation between portfolios is assumed to be 1?

Core-satellite: Since we are dealing with ‘active risk’ and not ‘total risk’ (stdev), we assume zero correlation because the managers active risk (tracking error) should be completely unrelated to one another. Corner Portfolios: In reality the correlation between asset classes is less than one. We assume that they are perfectly correlated (corr=1) w/no diversification benefits in order to take a more conservative route when determining whether the portfolio meets risk guidelines.