What is the best method for calculating VaR/CVaR for private equity, hedge fund, and alternative investment portfolios? I have only historical monthly return for them.
In my opinion using MC with Generalised Pareto should be better if is properly calibrated.This is because such a model would give higher probability mass in the tails. But of course the calibration will be as good as your historical data is, so the whole advantage of having higher probability of negative evolutions is actually based on an assumption (that the tails are well modeld by GPD).
The historical data approach is the most elegant since it is non-parametric (so no assumptions regarding the distribution are made).
If you look at VaR for portfolios, the copula approach should be considered as well.
You might find it useful to take a look at this article.