FRM Part I · FRM Exam Part I · Measures of Financial Risk
Which property distinguishes Expected Shortfall from Value-at-Risk as a risk measure?
Expected Shortfall is subadditive, so the ES of a combined portfolio never exceeds the sum of the component ES values. VaR can violate this, which is a key reason ES is considered a coherent risk measure.
- AES is always subadditive, so it satisfies the diversification property of a coherent measureCorrect
- BES ignores the size of losses beyond the threshold
- CES is always smaller than VaR at the same confidence level
- DES cannot be estimated by historical simulation
Explanation
ES is a coherent measure, including subadditivity, while VaR can violate it. ES accounts for tail magnitude, is at least as large as VaR at the same confidence, and can be estimated by historical simulation.
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