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FRM Part II · FRM Exam Part II · Credit Scoring and Retail Credit Risk Management

A bank holds 10,000 identical unsecured personal loans of 5,000 each. Each has a one-year PD of 3%, LGD of 70%, and defaults are independent. Expected loss on the portfolio is closest to which of the following, and what does independence imply about the risk of unexpected loss relative to a 10-loan corporate book of the same total size?

Expected loss is 50 million times 3% times 70%, which equals 1,050,000. Because the retail pool has thousands of small independent exposures, idiosyncratic risk diversifies away, so unexpected loss as a share of exposure is much smaller than for a concentrated corporate book of ten loans.

  1. A1,050,000; unexpected loss is proportionally much smaller because of diversificationCorrect
  2. B1,050,000; unexpected loss is proportionally much larger because of concentration
  3. C1,500,000; unexpected loss is proportionally much smaller because of diversification
  4. D350,000; unexpected loss is proportionally the same

Explanation

Exposure is 10,000 × 5,000 = 50,000,000. EL = 50,000,000 × 3% × 70% = 1,050,000. With many small independent exposures, idiosyncratic risk diversifies, so unexpected loss relative to exposure is far lower than for 10 large loans. 1,500,000 ignores LGD (50m × 3%); 350,000 is a wrong calculation.

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