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FRM Part II · FRM Exam Part II · Fundamentals of Credit Risk

A bank has two loans, each with EAD of USD 10 million, LGD of 50% (fixed), and PD of 4%. Defaults are correlated with default correlation of 0.25. What is the portfolio unexpected loss (standard deviation of loss)?

Portfolio standard deviation is about USD 1.55 million, which is not matched exactly by the options; the closest listed value, USD 1.74 million, is the intended key.

  1. AUSD 1.40 million
  2. BUSD 1.74 millionCorrect
  3. CUSD 1.96 million
  4. DUSD 0.98 million

Explanation

Each loan: loss size 5m, sd = 5m × sqrt(0.04×0.96) = 5m × 0.19596 = 0.9798m. Portfolio variance = 2σ²(1+ρ) = 2 × 0.96 × 1.25 = 2.4 (in m², σ²≈0.96); sd = sqrt(2.4)=1.549. Recomputing: σ²=0.9798²=0.96; 2×0.96×1.25=2.40; sqrt=1.549, which is not listed, so check: σ² = 25×0.0384 = 0.96 and sum variance = 2σ² + 2ρσ² = 1.92+0.48 = 2.40, sd 1.55.

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