The largest 10 losses over a 250 day observation period are as follows. Calculate the expected shortfall at a 98% confidence level:

The largest 10 losses over a 250 day observation period are as follows. Calculate the expected shortfall at a 98% confidence level:

20m

19m

19m

17m

16m

13m

11m

10m

9m

9m
A . 19.5
B . 14.3
C . 18.2
D . 16

Answer: C

Explanation:

For a dataset with 250 observations, the top 2% of the losses will be the top 5 observations. Expected shortfall is the average of the losses beyond the VaR threshold. Therefore the correct answer is (20 + 19 + 19 + 17 + 16)/5 = 18.2m.

Note that Expected Shortfall is also called conditional VaR (cVaR), Expected Tail Loss and Tail average.