Skip to content

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

A spectral risk measure assigns weights to quantiles of the loss distribution. Which weighting function property is required for the measure to be coherent?

A spectral risk measure is coherent when its weights are non-negative, integrate to one, and are non-decreasing in the loss quantile, so worse losses receive at least as much weight as milder ones. This risk-averse weighting ensures subadditivity and the other coherence axioms.

  1. AWeights must be non-decreasing in the loss quantile, so worse losses receive weights at least as large as smaller lossesCorrect
  2. BWeights must be equal across all quantiles
  3. CWeights must be zero for all quantiles above the VaR confidence level
  4. DWeights must be non-increasing in the loss quantile so that tail losses are discounted

Explanation

A spectral measure is coherent when the weights are non-negative, sum (integrate) to one, and reflect risk aversion, meaning weights do not fall as losses become worse. Equal weights give the mean, which is coherent but not risk averse, so the requirement is non-decreasing weights. Option C describes VaR-style truncation, which is not coherent.

Did you get it right without looking?

One question tells you little. A timed set on Measures of Financial Risk shows your real accuracy, how long you take and where you lose marks.

Practise Measures of Financial RiskFree diagnostic mock

More Measures of Financial Risk questions