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FRM Part II · FRM Exam Part II · Private Markets Investing

A direct lending fund has 10 equal loans of USD 10 million each. Each loan has a one-year default probability of 5% and zero recovery, and defaults are independent. Compared with a single USD 100 million loan with the same default probability and zero recovery, which statement about the one-year portfolio loss is correct?

Expected loss is USD 5 million in both cases, because 5% of USD 100 million is the same either way. Diversification across ten independent loans cuts the standard deviation of loss from about USD 21.8 million to about USD 6.9 million, so risk falls while expected loss is unchanged.

  1. AExpected loss is USD 5 million in both cases, but the diversified portfolio has a lower standard deviation of lossCorrect
  2. BExpected loss is lower for the diversified portfolio because defaults are independent
  3. CExpected loss is USD 5 million for the diversified portfolio and USD 50 million for the single loan
  4. DStandard deviation of loss is identical because expected loss is identical

Explanation

Expected loss: single = 5% × 100 = 5; portfolio = 10 × 5% × 10 = 5. Standard deviation: single = 100 × sqrt(0.05×0.95) ≈ 21.8; portfolio = 10 × sqrt(10 × 0.0475) ≈ 6.9. Diversification reduces volatility but not expected loss.

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