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FRM Part I · FRM Exam Part I · Calculating and Applying VaR

Which statement best describes a limitation of VaR that expected shortfall (ES) addresses?

VaR is not always subadditive and ignores the magnitude of losses beyond its threshold. Expected shortfall averages losses in the tail beyond VaR and satisfies the coherence properties, including subadditivity, so it captures tail severity and respects diversification better than VaR.

  1. AVaR is not subadditive in general and says nothing about the size of losses beyond the confidence level, whereas ES is coherent and averages tail lossesCorrect
  2. BVaR cannot be computed for portfolios containing options, whereas ES can
  3. CVaR requires normally distributed returns, whereas ES requires no distributional assumption of any kind
  4. DVaR is always lower than ES at a lower confidence level, which makes VaR unusable

Explanation

VaR can violate subadditivity, so diversification may appear to increase risk, and it ignores losses beyond the quantile. ES is the average loss beyond VaR and is a coherent measure. VaR can be computed for options using full revaluation or historical simulation, and it does not strictly require normality.

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