Explanation:
C is correct. The correct Basel II IRB credit risk capital for the portfolio is equal to:
(Exposure at Default * Loss given Default * DR<sub>99.9</sub>) − Expected Loss
where DR<sub>99.9</sub> is equal to the worst-case default rate for the portfolio of assets calculated using the Vasicek model. For retail credit cards, this calculation assumes a correlation of 0.04 between defaults on individual exposures, which is specified by the Basel committee.
The loss given default is equal to 1 minus the recovery rate, so it is 70%.
Therefore, the correct capital is (200 * 70% * 9.87%) − 4.2, or EUR 9.62 million.
A is incorrect. This uses the 1-year default rate at the 95% percentile.
B is incorrect. This uses the recovery rate instead of the loss given default and also forgets to subtract the expected loss.
D is incorrect. This forgets to subtract the expected loss.
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| Exposure at default | EUR 200 million |
|---|---|
| 1-year expected loss on the portfolio | EUR 4.2 million |
| Expected recovery rate on a defaulted credit | 30.00% |
| 1-year portfolio default rate at the 95<sup>th</sup> percentile | 5.66% |
| 1-year portfolio default rate at the 99.9<sup>th</sup> percentile | 9.87% |
What is the correct estimate of the Basel II credit risk capital that the bank should reserve for this portfolio?
A
EUR 3.72 million
B
EUR 5.92 million
C
EUR 9.62 million
D
EUR 13.82 million