standard dev of 2 corner portfolios combined

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tarik64

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may have missed this in the readigns but why when using corner portfolio’s can you calculate a portfolio’s std dev from 2 of the corner portfolio’s just by taking the weighted standard deviations of each… i thought you had to run it through the long equation of sq rt std1w1+std2w2+2w1w2std1std2cov12
 
pg 236
The linear approximation just illustrated provides a quick approximation (and upper limit) for the standard deviation; we also can apply this approximation in other cases in which we calculate efficient portfolios using the corner portfolio theorem.
If correlation = 1 ==> stddev = w1std1 + w2std2
if correlation is less than 1 ==> w1std1 + w2std2 + 2w1*w2*std1*std2*Rho12 would be lower.
 
or if imagined visually from return/risk EF graph, the approx is a straight line (linear) between corner ports but EF bows out to the left (meaning cor
 
Ideally, we should be using the long formula you mentioned, ie sq rt std1w1+std2w2+2w1w2std1std2cor12
However, for corner portfolios we can assume that the correlation between porfolios is 1. We can do this because the corner portfolios lie on the efficient frontier and hence are adequately diversified. This means that further diversification will not provide any major reduction in risk.
Note that this is still an approximation, the actual std of the portfolio might be lower. (albeit by a very small amount).
 
“we can assume that the correlation between porfolios is 1”

I think you mean correlations are zero for two corner portfolios .
Otherwise the net risk would be higher (!) than either of them for 1 correlation
 
janakisri wrote:
“we can assume that the correlation between porfolios is 1”

I think you mean correlations are zero for two corner portfolios .
Otherwise the net risk would be higher (!) than either of them for 1 correlation
Click to expand...
Can’t agree with you on this. Where is the weight?
Correlation is 1 if the frontier curve segment connecting 2 CPs is straight.
 
Yes you are correct . If the correlation is 1 , then the stdev is a linear combination of the two CP’s .
( Sorry I was mentally messed up in mixing up diversification with the corner portfolio idea . If you have correlation of zero and +ve weights you will have lower stdev for the combination i.e. higher diversification , but that is a totally different issue)
 
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