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

A portfolio has ten equally likely ordered loss outcomes (in USD million, from best to worst): -2, 0, 1, 2, 3, 4, 5, 6, 8, 10 (negative = gain). A risk manager uses a discrete spectral measure with weights on the worst four outcomes (10, 8, 6, 5) of 0.4, 0.3, 0.2, 0.1 respectively and zero elsewhere. What is the risk measure?

The spectral measure equals 0.4×10 + 0.3×8 + 0.2×6 + 0.1×5 = USD 8.1 million. This exceeds the simple average of the four worst losses, USD 7.25 million, because larger weights are placed on the most severe outcomes, reflecting risk aversion.

  1. AUSD 8.1 millionCorrect
  2. BUSD 7.25 million
  3. CUSD 9.0 million
  4. DUSD 2.5 million

Explanation

Weights sum to 1.0. Compute 0.4×10 + 0.3×8 + 0.2×6 + 0.1×5 = 4.0 + 2.4 + 1.2 + 0.5 = 8.1. The simple average of the worst four (7.25) ignores the risk-aversion weighting and is the equal-weight ES-style result.

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