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

A risk manager is testing whether a risk measure ρ is subadditive using two portfolios A and B. Which finding would demonstrate a violation of subadditivity?

A combined risk of 14 against stand-alone risks of 7 and 5 violates subadditivity, because the combined measure must not exceed the sum of 12. Values of 12 or 9 comply, and ρ(2A)=14 simply reflects homogeneity.

  1. Aρ(A+B) = 12, ρ(A) = 7, ρ(B) = 5
  2. Bρ(A+B) = 9, ρ(A) = 7, ρ(B) = 5
  3. Cρ(A+B) = 14, ρ(A) = 7, ρ(B) = 5Correct
  4. Dρ(2A) = 14, ρ(A) = 7, ρ(B) = 5

Explanation

Subadditivity requires ρ(A+B) ≤ ρ(A)+ρ(B) = 12. A combined value of 14 exceeds 12, a violation. A value of 12 meets it with equality and 9 shows diversification benefit. ρ(2A)=14 is consistent with homogeneity, not a violation.

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