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

A risk committee considers a spectral risk measure that places weights on the quantiles of the loss distribution. Which weighting function would make the measure coherent and reflect risk aversion?

A spectral risk measure is coherent with risk aversion when its weights are non-negative, sum to one and rise with loss severity, so worse outcomes receive more weight. A single-quantile weight gives VaR, which is not coherent, and declining weights contradict risk aversion.

  1. AWeights that are non-negative, sum to one and increase with the severity of the loss quantileCorrect
  2. BEqual weights on all quantiles, which gives the expected loss
  3. CZero weight on all quantiles except the 95th, which gives VaR
  4. DWeights that decline as losses become more severe

Explanation

A spectral measure is coherent when the weights are non-negative, integrate to one and are non-decreasing in loss severity, which expresses risk aversion. Equal weights give the mean, a single-quantile weight gives VaR (not coherent), and declining weights contradict risk aversion and break coherence.

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