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FRM Part I · FRM Exam Part I · Measuring Credit Risk

A portfolio holds two loans of 1,000,000 each with 100% loss given default. Each loan has a one-year default probability of 10%, and the default correlation is 0.20. What is the standard deviation of portfolio credit loss (to the nearest 1,000)?

The portfolio loss standard deviation is about 465,000. Each loan has a standard deviation of 300,000, and combining two with correlation 0.20 gives variance of 300,000 squared times 2.4, whose square root is roughly 464,758. Zero correlation would understate it.

  1. A424,000
  2. B465,000Correct
  3. C510,000
  4. D600,000

Explanation

Each loan's loss standard deviation is 1,000,000 × sqrt(0.1×0.9) = 300,000. Portfolio variance = σ²(2 + 2ρ) = 90,000,000,000 × 2.4 = 216,000,000,000, and the square root is about 464,758, or roughly 465,000. The 424,000 figure assumes zero correlation and 600,000 assumes perfect correlation.

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