I understand that portfolio variance is computed through $w'Cw$, where w is the vector of weights, $C$ being the covariance matrix. However, what I don't get is this: why can't this portfolio variance simply be calculated by observing the daily portfolio level returns and simply taking the variance of it? That would save the problem of having to compute a unwieldy large portfolio variance no?
I am asking in the context of Value-At-Risk (Parametric Method) - it is so named the variance-covariance method because it uses the covariance matrix explicitly - what I don't understand is why can't we do it in similar fashion to historical simulation (where correlation is factored implictly by just taking daily portfolio value data) and assuming a distribution over it. This is clearly simpler, but no finance book has proposed doing this for parametric VaR?
Please help me understand the difference thanks!