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

A loss distribution has five equally likely outcomes (20% each) in USD million: 2, 3, 5, 10, 20. A spectral risk measure assigns weights 0.1, 0.1, 0.2, 0.2, 0.4 to the losses sorted ascending (weights sum to 1). What is the risk measure?

The weighted sum is 0.2+0.3+1.0+2.0+8.0 = USD 11.5 million, which is higher than the equal-weighted expected loss of USD 8.0 million because worse outcomes receive more weight.

  1. AUSD 8.0 million
  2. BUSD 10.0 million
  3. CUSD 11.0 millionCorrect
  4. DUSD 20.0 million

Explanation

Compute 0.1(2)+0.1(3)+0.2(5)+0.2(10)+0.4(20) = 0.2+0.3+1.0+2.0+8.0 = 11.5. Check by parts: low three outcomes contribute 1.5, upper two contribute 10.0, total 11.5. The equal-weight expected loss is (2+3+5+10+20)/5 = 8.0, which ignores risk aversion.

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