Corner Portfolios - Estimated Standard Deviation

K

kimc

New member
Joined
Jun 18, 2026
Messages
0
Reaction score
0
In all of the Schweser corner portfolio example problems, the answer key “estimates standard deviation” by simply taking the weighted average of the portfolio standard deviations.
But when I calculated it my way (I think.. the correct way), the estimates are ocassionally off by ~100bps.
Schweser says:
Take weighted average of SD’s as an estimate -=- I’m pretty sure this overstates standard deviation..
The way I learned:
Assuming correlation is zero, it is sqrt(W^2*SD^2 + W^2*SD^2)
—
I’m worried about a situation where the estimated SD is too risky for the IPS using the Schweser method, but meets risk requirements under the “way I learned method”. In this scenario, do I move down to another corner portfolio or stick with the original weights?
*Please excuse the crappy formula formatting above…
 
Yes, the weighted average does overstate the exact SD, but it should not be in the 100-200 bp range.
 
For example:
W1 = 20% SD1 = 12.1%
W2 = 80% SD2 = 9.0%
I get an estimated 9.62% and using the variance formula, I get 7.59%.
What am I doing wrong? It’s bugging me and I can’t figure it out.
 
Try assuming the corellation is 1, not zero – that last term should bring you up to a more reasonable looking value:
sqrt[(W^2*SD^2) + (W^2*SD^2) + (2*W*W*SD*SD*1)]
 
GKon17 wrote:
Try assuming the corellation is 1, not zero – that last term should bring you up to a more reasonable looking value:
sqrt[(W^2*SD^2) + (W^2*SD^2) + (2*W*W*SD*SD*1)]
Click to expand...
^This sounds correct, I vaguely remember one of the assumptions being a perfect correlation
 
Wait so which one do we use for the test? The same variance formula or the weighted average method?
 
assuming correlation is 0 creates a higher standard deviation figure which is more conservative.
Assume zero for the exam
 
Hi there – I think that might be backwards…. Assuming a perfect correlation of 1 would be the riskiest (most conservative) assumption, wouldn’t it? That’s why we seek out investments w/ correlations less than 1 for diversification purposes.
Either way, though – just do a weighted average for these. Correlation assumptions be damned!
 
Wouldn’t a correlation of 1 mean the dispersion of returns is less than if they had zero correlation?
Brain is tired…. need a break
 
if 1 is used as the correlation, then it is weighted-average.
I assume there is diversification between the two, so use variance, wouldn’t we?
 
if 1 is used as the correlation, then it is weighted-average.
I assume there is diversification between the two, so use variance, wouldn’t we?
 
99% of the time…… i think its the way they want you to learn it, is to just use the weighted average to find the standard deviation. They do mention that this estimate overstates true standard deivaiton because it does not account for diversifcicaiton (correlation) between the 2 corner portfolios.
 
Kimc: Rest assured you have done nothing wrong. The approximation works very well if the correlation between the 2 portfolios is high. As the correlation drops, the approximation gets worse.
You can think of the approximation as a “worst case” standard deviation. If the correlation is provided, then by all means use the exact formula.
 
You must log in or register to reply here.
Back
Top