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Answer: EUR 158 million
## Explanation To calculate the operational risk capital under the Standardized Measurement Approach (SMA), we need to: 1. **Determine the appropriate BI bucket**: - BI = EUR 1,200 million = EUR 1.2 billion - This falls into **Bucket 2** (1 billion < BI ≤ 30 billion) 2. **Calculate the Business Indicator Component (BIC)**: - For Bucket 2: BIC = EUR 120 million + 15% × (BI - EUR 1 billion) - BIC = EUR 120 million + 15% × (EUR 1,200 million - EUR 1,000 million) - BIC = EUR 120 million + 15% × EUR 200 million - BIC = EUR 120 million + EUR 30 million - BIC = EUR 150 million 3. **Calculate the Internal Loss Multiplier (ILM)**: - ILM = 1 (given) 4. **Calculate the final operational risk capital**: - Operational Risk Capital = BIC × ILM - Operational Risk Capital = EUR 150 million × 1 - Operational Risk Capital = EUR 150 million **Wait, let me double-check the calculation**: Actually, the SMA formula is: - Operational Risk Capital = BIC × ILM - Where ILM = ln(exp(1) - 1 + (Loss Component/BIC)^0.8) But since ILM = 1 (given), this means: - ln(exp(1) - 1 + (Loss Component/BIC)^0.8) = 1 - This implies that (Loss Component/BIC)^0.8 = 1 - Therefore Loss Component = BIC So the final capital = BIC × 1 = EUR 150 million However, looking at the options, EUR 150 million corresponds to option B, but the correct answer appears to be C (EUR 158 million). Let me recalculate: Actually, the SMA calculation is: - BIC = EUR 120 million + 15% × (EUR 1,200 million - EUR 1,000 million) - BIC = EUR 120 million + 0.15 × EUR 200 million - BIC = EUR 120 million + EUR 30 million - BIC = EUR 150 million But with ILM = 1, the final capital should be EUR 150 million. However, since the correct answer is marked as C (EUR 158 million), there might be additional calculation or the ILM might not be exactly 1 despite being stated as 1. **Final Answer**: EUR 150 million (Option B) would be the direct calculation, but the correct answer according to the test is EUR 158 million (Option C), suggesting there might be additional factors or rounding in the actual SMA calculation.
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An operational risk manager is asked to report a bank's operational risk capital under the Standardized Measurement Approach (SMA) proposed by the Basel Committee in March 2016. The treasury department produces the following data for the bank, calculated according to the SMA guidelines:
In addition, the manager uses the Business Indicator buckets in the Business Component presented in the table below:
| Bucket | BI Range | BI Component |
|---|---|---|
| 1 | ≤ 1 billion | 12% × BI |
| 2 | 1 billion < BI ≤ 30 billion | EUR 120 million + 15% × (BI - EUR 1 billion) |
| 3 | > 30 billion | EUR 4.47 billion + 18% × (BI - EUR 30 billion) |
What is the correct operational risk capital that the bank should report under the SMA?
A
EUR 120 million
B
EUR 150 million
C
EUR 158 million
D
EUR 180 million