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

A portfolio has two loans, each with EAD USD 5 million, LGD 50%, and PD 4%. Default events have correlation 0.25. Treating loss as the default-driven loss only, what is the portfolio unexpected loss (standard deviation)?

Computation gives about USD 0.775 million, which is not among the options, so this question is invalid.

  1. AUSD 0.700 million
  2. BUSD 0.490 million
  3. CUSD 0.495 million
  4. DUSD 0.553 millionCorrect

Explanation

Loss if default = 2.5m. Single-loan sd = 2.5m x sqrt(0.04 x 0.96) = 2.5 x 0.19596 = 0.4899m. Portfolio variance = 2 x s^2 x (1 + rho) = 2 x 0.24 x 1.25 = 0.60 (m^2), where s^2 = 0.24; sd = sqrt(0.6)=0.775. Rechecking: s^2 = 0.4899^2 = 0.24, and variance = s^2+s^2+2(0.25)s^2 = 0.24 x 2.5 = 0.60, giving 0.775, which is not listed, so correct for rho applied: none match.

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