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FRM Part II · FRM Exam Part II · Portfolio Risk: Analytical Methods

Which statement about VaR as a risk measure for portfolios is correct?

VaR only marks the loss threshold at a confidence level and conveys nothing about how bad losses are beyond it, whereas expected shortfall averages those tail losses. VaR is not always subadditive, so it is not coherent.

  1. AVaR is subadditive for every return distribution, so portfolio VaR never exceeds the sum of standalone VaRs
  2. BVaR says nothing about the size of losses beyond the confidence threshold, unlike expected shortfall which averages those tail lossesCorrect
  3. CExpected shortfall at 99% is always smaller than 99% VaR
  4. DVaR is a coherent risk measure because it satisfies monotonicity, translation invariance, homogeneity and subadditivity

Explanation

VaR is a quantile and ignores the severity of tail losses beyond it; expected shortfall averages them. VaR can violate subadditivity for non-elliptical distributions, so it is not coherent, and ES is at least as large as VaR at the same level.

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