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Definition of Expected shortfall

A

ALEX_AK

Member
What is the exact definition of expected shortfall when it is being mentioned in the exams?
I have seen that it is being referred to as TVaR in several context. But TVaR and ES are different measures according to the core reading.
 
They are slightly different measures and beware there are many ways of defining these values (especially ES).

Also, be careful about comparing the two as they are doing something different as defined in McNeil. It's also tricky as ES has little intuitive meaning.

The way I look at it, if we have T policies:
  • TVAR is the average excess loss per policy that incurred losses over the VAR threshold.
  • ES is the average loss over the threshold per policy (regardless if it is in the tail or not)

So, ES might be more helpful, eg if you readily wanted to know what your total losses over the VAR threshold might be if the number of policies changed.
 
Hi Simon,

Thanks a lot for the reply.

I saw a question, "Compare value at risk and expected shortfall".
In the solution, the answer talks about VaR and TVaR.

So do we assume that when expected shortfall is mentioned (without any elaboration on its definition or formula), the examiner is referring to TVaR?
 
Hello,
I am looking at Q4.19i in Q&A Part 4 of 2018 examinations. I understand that all of the Q&A are now part of the core reading.
 
Hi. The Q&A is not Core Reading. I would also advise making sure you have the various upgrades to the 2018 CMP.
I think in this question, it is getting at the difference between VaR, the point estimate of the maximum loss, and ES as the loss beyond that point (ES/TVaR trying to do the same thing).
I'd hope in an exam, the examiners would be quite specific if it was critical to the question.
 
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