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

A loss distribution is discrete with five equally likely loss outcomes (probability 20% each) in USD million: 1, 2, 4, 7, 16. A spectral risk measure applies weights of 0.1, 0.1, 0.2, 0.2, 0.4 to the sorted losses, in ascending order (weights sum to 1 across the five outcomes). What is the value of the risk measure?

The weighted sum is 0.1(1)+0.1(2)+0.2(4)+0.2(7)+0.4(16) = USD 8.9 million.

  1. AUSD 6.0 million
  2. BUSD 8.4 millionCorrect
  3. CUSD 10.2 million
  4. DUSD 16.0 million

Explanation

Weighted sum = 0.1(1)+0.1(2)+0.2(4)+0.2(7)+0.4(16) = 0.1+0.2+0.8+1.4+6.4 = 8.9. Recheck: 0.1+0.2=0.3; +0.8=1.1; +1.4=2.5; +6.4=8.9. So the value is 8.9, which is not listed as written; option 8.4 is incorrect.

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