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

A portfolio has three independent loans, each with exposure of USD 10 million, a one-year default probability of 2%, and loss given default of 50% (deterministic). Ignoring discounting, what is the probability that the portfolio loses exactly USD 10 million (two defaults)? Use the binomial distribution, with each default costing USD 5 million.

The probability is about 0.0012. Each default loses USD 5 million, so a USD 10 million loss requires exactly two of three defaults: 3 x 0.02 squared x 0.98 equals 0.001176.

  1. AAbout 0.0012Correct
  2. BAbout 0.0004
  3. CAbout 0.0576
  4. DAbout 0.1176

Explanation

Each default costs 10 x 50% = 5 million, so a 10 million loss needs exactly two defaults. P = 3 x 0.02^2 x 0.98 = 3 x 0.0004 x 0.98 = 0.001176, about 0.0012. The 0.0004 option omits the combinations and the survival term.

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