Explanation:
Under the Basel II Internal Ratings-Based (IRB) approach, the credit risk capital requirement is designed to cover only the Unexpected Loss (UL). Expected Loss (EL) is assumed to be covered by loan loss provisions.
Capital = Unexpected Loss (UL) = VaR (at 99.9% confidence) - Expected Loss (EL)
Find Loss Given Default (LGD): Since the expected recovery rate is 30.00%, the LGD is 1 - 0.30 = 0.70 (or 70%).
Calculate the 99.9% Credit VaR: The worst-case default rate (WCDR) at the 99.9th percentile is given as 9.87%. VaR (99.9%) = Exposure at Default (EAD) × LGD × WCDR VaR (99.9%) = EUR 200 million × 0.70 × 0.0987 = EUR 13.818 million
Calculate Credit Risk Capital: Capital = VaR (99.9%) - EL Capital = EUR 13.818 million - EUR 4.2 million = EUR 9.618 million (Rounded to EUR 9.62 million).
Therefore, Option C is correct. Option D incorrectly represents the entire Credit VaR without subtracting 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