Level 2: Post what your remember here...

[David Harper CFA FRM]

Hi cqbzxk, but i never said that (i have not seen the source exam question, i suggested that if it asked for ES and included VaR, the VaR is a red herring). In my experience, the #1 confusion in regard to ES is the mistaken idea that it has some relationship to VaR. It does not. A 95% ES is the (conditional) average of the worst 5% (of the distributional tail), period. A 95.5% ES is the average of the worst 4.5%. We identify the distribution, we find the 1-confidence = signficance% tail, and we translate that tail into its own probability distribution such that its mean (weighted within the tail distribution only) is the ES. The 95% VaR is a quantile, it plays no role is this calculation. The confusion typically reduces to a confusion about the meaning of a conditional mean; it does not mean conditional on VaR! We may simultaneously want both the 95% VaR and the 95% ES, but the ES does not need anything from the VaR. Thanks,

 

[David Harper CFA FRM]

I forget (is another reason i regret trying to decipher these partial question snippets) that we can estimate ES by taking an average of the tail VaRs, per Dowd Chapter 3 (Dowd 3.4.1). That is an instance of using easier-to-access VaRs (quantiles) as a means to approximate the conditional (tail) mean, but I have no clue if this question was looking for that approach, having yet to see the actual question thanks,