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Expected shortfall (ES) -- GARP's EOC Question 1.19

Expected Shortfall.jpg
Hi David. I am having trouble with understanding this question and answer 1.19 related to Expected Shortfall in Book 4 chapter 1 Measures of Financial Risk, page 12.
Specifically, I am unable to understand this term (0.05-0.0009-0.0042)*9 and why it is added here. I was wondering if you could help me with this.

Expected Shortfall.jpg

David Harper CFA FRM

David Harper CFA FRM
Staff member
Hi @rajivbangalore25 See image below; this is from a simple XLS I made for for you here at https://www.dropbox.com/s/kp4wp27o3k0cmwg/garp-p1-t4-eoc-1-19.xlsx?dl=0

btw, these are good questions by GARP. Per the lower panel (their question 1.19), we need the (conditional) average of the 5.0% tail given we want a 95.0% confident ES. So we don't need the entire 5.400%, we need (5.0% - 0.090% - 0.420%) = 4.490% of the third loss bin, so that we can compute a weighted average. Let me know if you need more help, the XLS should explain, and you should be able to edit 95% to something like 96.0% ES (and the result does change). You can see that I agree with GARP's answer; further, notice I have shown both P/L and L/P formats. Thanks,

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