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

A risk committee compares two risk-aversion profiles for an exponential spectral risk measure, with risk-aversion coefficient k. Moving from a low k to a high k, which outcome is expected for the measure on the same loss distribution?

As the risk-aversion coefficient rises, the exponential spectral measure puts more weight on the worst losses, so the measure increases toward the maximum loss. At low risk aversion the weights become nearly equal and the measure approaches the mean loss.

  1. AThe weights on the worst losses increase relative to milder losses, so the measure risesCorrect
  2. BThe measure falls because weights are spread more evenly across all outcomes
  3. CThe measure is unchanged because the weights always sum to one
  4. DThe measure converges to the mean loss

Explanation

A higher k concentrates more weight on the worst tail outcomes, so the weighted average of losses rises, approaching the maximum loss as k grows. A low k spreads weights nearly evenly, approaching the mean. Weights summing to one does not make the measure invariant to their allocation.

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