Let's say you want to calculate a VaR for a portfolio of 1000 stocks. You're really only interested in the left tail, so do you use the whole set of returns to estimate mean, variance, skew, and shape (let's also assume a skewed generalized error distribution - SGED)? Or would you just use the left tail (let's say the bottom 10% of returns)?
For some reason, using the whole set of returns seems more correct to me (by using only the left 10% or returns you'd really be approaching a non-parametric VaR). But using the whole set of returns would likely cause some distortion in the left tail in order to get a better fit elsewhere.
How are the pros doing this? Thanks!