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P1.T4.411. Expected shortfall (ES)


Well-Known Member
Hi All,

I am referring to question 411.3 from the quiz: Can someone please tell how to get to the loss of 200,000; 150,000 and 110,000 respectively?

411.1: I am wondering why for this question only the worst four losses are relevant for the ES? It has nothing to do with the prob. weights, because they only signal how likely the loss will be, but have no influence on the ES.
The choice of the worst four losses is in contrast to question 409.1 where we also have a 95% confidence interval, but take the worst five losses.

Any input is highly appreciated.

Thank you!

Nicole Seaman

Director of FRM Operations
Staff member
Hello @emilioalzamora1

Please make sure to post your questions in the original forum post. The forum links are on each answer page in the PDF that can be downloaded on the Quiz page in the study planner. Here are the forum links that correspond to these questions:
If your questions have not already been answered on those forum threads, please post them there.

Thank you,


David Harper CFA FRM

David Harper CFA FRM
Staff member
Hi @emilioalzamora1

Re 411.3, please see the answer because I added an image (and XLS) to give additional help: https://www.bionicturtle.com/forum/threads/p1-t4-411-expected-shortfall-es.8075/
ie., there is a 10% probability of two loss events, so the worst outcome is a loss of $200,000 with probability = 10% * 10% * 10%
The next worst outcome is a loss of $150,000 due to two losses, one for $100,000 and one for $50,000, with probability = 10% * 10* 20% *2
(* 2 because it can be either sequence, 100K then 50k or 50k then 100k)

Re: 411.1. The probabilities do determine the ES. 95.0% ES is the conditional average of the 5.0% probability tail, which consists of the worst four losses: 0.5% + 1.0% + 1.5% + 2.0% = 5.0%

Re: 409.1: same logic, 95.0% ES retrieves the average of the worst 5.0%, but as this is simple HS, each loss is 1.0%, so the worst 5 are the worst 5.0%

I hope that clarifies!