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FRM Part II · FRM Exam Part II · Estimating Market Risk Measures: An Introduction and Overview

A portfolio has 200 daily historical P&L observations. The five worst losses (in USD thousands) are 410, 350, 320, 290 and 260, and the sixth worst is 240. Using the convention that VaR at 97.5% confidence is the loss at the 5th worst observation (5 of 200 = 2.5% tail), and expected shortfall is the average of the tail losses beyond and including that tail set of 5 observations, what is the expected shortfall?

Expected shortfall is 326 thousand USD. It is the average of the five tail losses (410, 350, 320, 290, 260), which sum to 1,630, divided by 5. The figure 260 is only the VaR cutoff, not the tail average.

  1. A260
  2. B326Correct
  3. C294
  4. D410

Explanation

The tail set is the five worst losses: 410, 350, 320, 290, 260. Sum = 1,630; divided by 5 = 326. Choosing 260 gives the VaR, not ES. Using 4 observations gives 342.5, and averaging with the sixth gives 311.7. The 410 figure is only the maximum loss.

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