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FRM Part II · FRM Exam Part II · Parametric Approaches (II): Extreme Value

Using a POT model with threshold u = 2.0%, shape ξ = 0.2 and scale β = 0.5, a risk manager has computed a 99% VaR of 2.95%. Using ES = (VaR + β − ξu)/(1 − ξ), what is the 99% expected shortfall?

Expected shortfall is about 3.81%. The numerator is VaR plus β minus ξ times u, which is 2.95 + 0.5 − 0.4 = 3.05, and dividing by 1 − ξ = 0.8 gives 3.81%. ES exceeds VaR because it averages losses beyond the VaR.

  1. AApproximately 3.81%Correct
  2. BApproximately 4.31%
  3. CApproximately 2.54%
  4. DApproximately 3.45%

Explanation

The numerator is 2.95 + 0.5 − 0.2 × 2.0 = 3.05. Dividing by 1 − ξ = 0.8 gives 3.8125, about 3.81%. Omitting the ξu adjustment gives 4.31%. Dividing by 1 + ξ instead gives 2.54%. VaR + β gives 3.45%, which ignores the tail-heaviness scaling.

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