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FRM Part I · FRM Exam Part I · Common Univariate Random Variables

A risk analyst models a loss L as continuous uniform on [0, 200] (USD thousands). What is the 95% expected shortfall of L, defined as the expected loss given that the loss is at or beyond the 95% VaR?

The 95% expected shortfall is 195 thousand USD. The 95% VaR is 190, and the worst 5% of outcomes are uniform between 190 and 200, so their average is the midpoint of that tail, 195. VaR itself is 190, not ES.

  1. A190.0
  2. B195.0Correct
  3. C197.5
  4. D200.0

Explanation

The 95% quantile is 0.95 x 200 = 190. The tail is uniform on [190, 200], whose mean is (190+200)/2 = 195. The VaR value of 190 is not the ES; 197.5 would be the 97.5% ES-type midpoint error.

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