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FRM Part II · FRM Exam Part II · Credit Value at Risk

A portfolio has two loans, each with exposure USD 10 million, loss given default of 60%, and one-year default probability of 2%. Defaults are independent. What is the portfolio expected loss and the probability that both loans default?

Each loan's expected loss is 10 million times 60% times 2%, or USD 0.12 million, so the portfolio is USD 0.24 million. With independence, both default with probability 2% times 2%, which is 0.04%.

  1. AExpected loss USD 0.24 million; joint default probability 0.04%Correct
  2. BExpected loss USD 0.12 million; joint default probability 0.04%
  3. CExpected loss USD 0.24 million; joint default probability 4%
  4. DExpected loss USD 0.24 million; joint default probability 0.02%

Explanation

Each loan EL = 10 x 0.6 x 0.02 = 0.12 million; two loans give 0.24 million. Independent joint default = 0.02 x 0.02 = 0.0004 = 0.04%. Adding probabilities (4%) is the mistake for joint default; 0.12 is only one loan.

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