How many data points are required to perform a fitting of GPD?

Question

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

1. if that's enough?
2. 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).

Answer 1

Playing around with some random numbers from the GPD, I'm not convinced that a sample of 10 will give anything like useful results.

The code for generation was

require("gPdtest")
reps = 10000
ValuesAct = rgp(reps, 0.5,0.5)
plot(density(ValuesAct))
quantile(ValuesAct, probs=0.999)

loops = 10000
results = matrix(rep(NA,2*loops), ncol = 2)
colnames(results) = c("shape", "scale")

for(i in 1:loops)
{
  ValuesSample = sample(ValuesAct,10,replace=F)
  results[i,] = gpd.fit(ValuesSample, "amle")
}

plot(density(results[,2]))
lines(density(results[,1]), col = "green")
abline(v=0.5)
legend("topright", c("Shape", "Scale"), col = c("green", "black"), lwd=1)

Answer 2

Given a sample you can estimate the parameters and calculate the standard deviation of these estimations. You could use this as a measure of quality.

Creating a measure given only the sample size $N$ seems very hard to me since the quality of the estimation may depend on the values of the parameters.