A friend of mine told me that their firm is using Extreme Value Theory (EVT) to compute value of the Expected Shortfall 99% of a portfolio for their asset allocation process. To do so, they try to fit the parameters of the Generalized Pareto Distribution using the historical sample of their portfolio, and they use a formula to get the value of $ES_{0.99}$.
However, I they are using monthly data points, which means that the size of the sample is pretty (very) limited. When I asked what the minimum number of point required to performed the fitting was, I was told that their algorithm was asking for a minimum of 10 points.
I am wondering
- if that's enough?
- how could we compute some kind of quantitative value indicating "how wrong" the fitting might be given the give size of the sample $N$? (this method could be specific to GPD, but of course a generic approach would be great).