VaR and CVaR Methods for Alternative Investment Portfolios

Summary

The document compares ways to estimate value at risk and conditional value at risk when only monthly historical returns are available for private equity, hedge fund, and other alternative investment portfolios. It presents historical simulation as a nonparametric option, avoiding an assumed return distribution, and suggests Monte Carlo simulation with a generalized Pareto tail model as a way to represent more probability in extreme outcomes.

These methods depend on the quality and length of the available data. The generalized Pareto approach is only as credible as its calibration and the assumption that the tail follows that distribution. For portfolio risk, the answer also recommends considering dependence between assets through a copula. The response offers directions to consider rather than a worked calculation, comparative test, or evidence that one method performs best in a particular setting.

Key ideas

• Historical simulation estimates risk without specifying a return distribution.
• Monte Carlo simulation with a generalized Pareto model can represent heavier tails if calibrated appropriately.
• Tail estimates remain dependent on the data and the validity of the assumed tail model.
• Copulas may help represent dependence when estimating risk for portfolios.

Tags

# How to calculate VaR/CVaR for private equity, hedge fund, and alternative investment portfolios?


# How to calculate VaR/CVaR for private equity, hedge fund, and alternative investment portfolios?












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.

## Answer by KAT (score 2, accepted)

https://quant.stackexchange.com/a/8648

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.

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