Standard deviation of a portfolio

[lylcheng88]

Hey guys, I know this is a pretty basic concept but Question #4 in the Schweser self-test is quite confusing.
I thought the standard deviation of a portfolio needs to be calculated as the sq rt of W1^2*Std Dev1 + W2^2*Std Dev2 + 2*W1*W2*Cov(1,2)
However, why does the answer to this question simply take the weighted average of the two portfolios’ Std dev as the gross portfolio std dev?

 

[S2000magician]

They’re assuming that the correlation of returns of adjacent corner portfolios is zero.
That’s probably wrong, but that’s the assumption.

 

[ABAL]

On another note, that’s the very definition of corner portfolio. 2 corner portfolios are the 2 ends of segmentation (blah!), hence the supposedly have 0 correln. (blah! blah!)

 

[lylcheng88]

Thanks to you both - are corner portfolios supposed to have 0 correlation on a presumptive basis? I find this kind of strange but if the textbook specifies this somewhere please could someone enlighten me to read up more on this?

 

[S2000magician]

Yes: it’s a simplifying assumption.
In fact, there’s no reason for them to have zero correlation of returns.

 

[lylcheng88]

S2000magician wrote:
Yes: it’s a simplifying assumption.
In fact, there’s no reason for them to have zero correlation of returns.

Thank you! really appreciate your help!

 

[S2000magician]

My pleasure.