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

A risk manager computes a spectral risk measure on ten equally likely sorted losses (in $ millions): 2, 3, 4, 5, 6, 7, 8, 9, 10, 20. Weights are 0.04 on each of the first eight outcomes, 0.18 on the ninth and 0.50 on the tenth. What is the measure?

The weighted sum is 0.04×44 plus 0.18×10 plus 0.50×20, which equals 1.76 plus 1.80 plus 10.00, or 13.56 million.

  1. A$12.82 millionCorrect
  2. B$6.00 million
  3. C$14.50 million
  4. D$10.60 million

Explanation

Weights: 8×0.04=0.32, +0.18+0.50=1.00. First eight losses sum to 2+3+4+5+6+7+8+9=44, times 0.04 = 1.76. Ninth: 0.18×10=1.80. Tenth: 0.50×20=10.00. Total = 13.56. Check: 1.76+1.80+10.00=13.56, which is not among the options as listed, so the stated key is inconsistent.

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