When calculating the standard deviation using 2 weighted corner portfolios, why is the standard deviation of the two equal to their weighted average, and not Var(X+Y)=(w1)^2*(Var(X))+(1-w)^2*(Var(Y))?
For example, Corner Portfolios 1 and 2 are weighted w=20% and 80%, so their standard deviation is .2*std1+.8*std2.
corr between 2 cp’s is 0.
Perfect answer. It s what I am looking for. Thanks!
Not true…
You assume correlation is 0 to simplify the standard deviation calc which actually creates an overall higher standard deviation calc - an upper bound so to say.
You would need a lot of covariances to calculate the standard deviation of the assets in each CP which is why you simplify the calculation.
Actually I thought you assume correlation between 2 CP’s is 1? Then you can just use the weighted average of the standard deviation.
If the correlation is assumed to be 0, then you get Var = w1^2*StDev1^2 + w2*Stdev2^2
Do not make it more complicated as it is.
Remember for the exam: sigma portfolio = w1 x sigma1 + w2 x sigma2
And yes, the estimate overstates the true sigma.