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

A risk committee wants a risk measure that is coherent and gives more weight to larger losses by weighting quantiles. Which approach matches this goal?

A spectral risk measure with non-negative weights that rise with the severity of the loss quantile is coherent and reflects risk aversion. Expected shortfall is a special case with equal weights on the tail.

  1. AUse 99% VaR with a longer holding period
  2. BUse a spectral risk measure with a non-decreasing weighting of tail quantilesCorrect
  3. CUse standard deviation of returns as the risk measure
  4. DUse VaR with a risk-averse scaling factor applied to the quantile that decreases with the loss size

Explanation

A spectral risk measure is a weighted average of loss quantiles; it is coherent if the weights are non-negative, sum to one and are non-decreasing in the loss quantile (reflecting risk aversion). VaR and standard deviation are not coherent in general.

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