Skip to content

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

A loss L takes values 0, 10 and 20 with probabilities 0.36, 0.48 and 0.16. A distortion risk measure is defined as ρ(L) = ∫ g(S(x)) dx over x ≥ 0, where S(x) = P(L > x) and the distortion function is g(s) = √s. What is ρ(L)?

The distortion measure equals 12. The survival function is 0.64 on (0,10) and 0.16 on (10,20), and applying the square-root distortion gives 10×0.8 + 10×0.4 = 12. This exceeds the expected loss of 8 because g inflates tail probabilities.

  1. A8
  2. B16
  3. C12Correct
  4. D20

Explanation

S(x) = P(L > x) = 0.64 for 0 ≤ x < 10 and 0.16 for 10 ≤ x < 20. So ρ = 10·√0.64 + 10·√0.16 = 10(0.8) + 10(0.4) = 12. The expected loss is 10(0.64) + 10(0.16) = 8, which is g(s) = s. Weighting the 20 outcome by 0.4 over its whole range gives 16, which is wrong because S must be integrated by interval.

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