When calculating the standard deviation of a portfolio consisted of twe corner portfolios, why we just need to simply use the weight average of corner portfolio’s standard deviation, no need to consider the correlation between the two corner portfoilos?
We just make the assumption that the correlation is 1 between the 2 corner portfolios. This greatly simplifies the calculation of standard deviation of the mix amd allows us to just use the weighted average standard deviations of the constituent corner portfolios.
Saying as more often than not the actual correlation between the corner portfolios will be less than 1, using the weighted average method actually slightly overestimates the standard deviation of the mix.
An over estimation is considered far more acceptable than an underestimation and the value found can serve as a “maximum” standard deviation calculation.
Properly, we should consider the correlation of returns between adjacent corner portfolios.
Practically, as S666 correctly states, we’re assuming that it’s 1.0 at the risk of overestimating the standard deviation of returns.