Are there any results for calculating the variability in the Expected Shortfall measure. I am looking for Large sample confidence intervals under Normality for Expected Shortfall or calculation of standard error for the same.


I wrote this paper a couple of years ago where we discuss this kind of topic.

On page 6, you see a formula that comes from a paper from Acerbi available in Szego's book:

$$\sigma^2(ES^{(N)}_\alpha(X)) \overset{N>>1}{=} \frac{1}{N(1-\alpha)^2} \int_0^{F^{-1}(1-\alpha)} dx \int_0^{F^{-1}(1-\alpha)} dy \{ \min( F(x), F(y) ) - F(x)F(y) \}$$

This should be a good starting point and reference for you to derive the confidence interval.


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