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FRM Part I · FRM Exam Part I · Measures of Financial Risk

Which statement about VaR as a risk measure is correct?

VaR identifies a loss level exceeded with a small probability but gives no information about how large losses could be beyond that level. Expected shortfall measures average tail loss, and VaR is not always subadditive.

  1. AVaR states a loss threshold but says nothing about the size of losses beyond itCorrect
  2. BVaR is always subadditive, so diversification can never increase it
  3. CVaR measures the expected loss given that VaR is exceeded
  4. DVaR at 99% over one day is always larger than VaR at 95% over ten days

Explanation

VaR gives only the quantile of the loss distribution, so tail severity beyond it is not captured; expected shortfall addresses that. VaR is not generally subadditive, and the expected loss beyond VaR is expected shortfall. The comparison of 99% one-day and 95% ten-day VaR depends on the data.

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