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

A bank's risk committee compares VaR with expected shortfall (ES) for a portfolio containing short option positions with a highly skewed, fat-tailed P&L. Which statement best explains why VaR may be an inadequate sole measure for this portfolio?

VaR is inadequate here because it ignores how large losses are beyond the quantile and is not generally subadditive, so with skewed, fat-tailed option P&L it can understate tail risk. Expected shortfall captures the tail average and is coherent.

  1. AVaR is not expressed in monetary units, so it cannot be compared across desks
  2. BVaR is always larger than ES at the same confidence level, so it overstates risk
  3. CVaR cannot be computed for portfolios containing options
  4. DVaR ignores the magnitude of losses beyond the quantile and is not subadditive in general, so it can understate tail risk and diversification effectsCorrect

Explanation

VaR reports only the loss threshold, not the size of tail losses, and for non-elliptical distributions it can violate subadditivity. ES at the same confidence level is at least as large as VaR, so the option claiming VaR exceeds ES is wrong. VaR is in monetary units and can be computed for options.

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