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

A credit portfolio has an expected loss of USD 12 million. Its 99.9% one-year credit loss quantile is USD 87 million, and the standard deviation of losses is USD 20 million. The bank holds economic capital to cover unexpected losses at the 99.9% confidence level. What is the economic capital, and what is the ratio of this capital to the loss standard deviation?

Economic capital covers unexpected loss, which is the 99.9% loss quantile less expected loss: USD 87 million minus USD 12 million, or USD 75 million. Dividing by the USD 20 million standard deviation gives 3.75. Using the full quantile or adding expected loss is incorrect.

  1. AUSD 75 million; ratio 3.75Correct
  2. BUSD 87 million; ratio 4.35
  3. CUSD 75 million; ratio 4.35
  4. DUSD 99 million; ratio 4.95

Explanation

Economic capital = credit VaR minus expected loss = 87 - 12 = USD 75 million. Ratio = 75/20 = 3.75. Using the full 87 ignores that expected loss is covered by provisions and pricing. Adding EL gives 99, which is the wrong sign.

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