Explanation:
The Expected Shortfall (ES) at a given confidence level is calculated as the average of the VaR values for confidence levels strictly greater than . We slice the tail (from 96.5% to 100%) into equal probability intervals. Here, we can use the provided VaR estimates at 97.0%, 97.5%, 98.0%, 98.5%, 99.0%, and 99.5%.
Sum of VaR values = $211,425,000 + 222,233,500 + 233,562,500 + 241,523,000 + 256,300,000 + 280,500,000 = 1,445,544,0001`,445,544,000 / 6 = 240,924,000$.
Therefore, the closest estimate for the daily ES at the 96.5% confidence level is USD 240,924,000.
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Q.73 An investment bank has USD 42 billion in assets. The bank’s CRO computes the daily VaR at various levels of confidence as follows:
| Confidence Level | VaR (USD) |
|---|---|
| 90.0% | 125,555,000 |
| 95.0% | 180,250,500 |
| 95.5% | 185,000,500 |
| 96.0% | 195,500,000 |
| 96.5% | 203,205,500 |
| 97.0% | 211,425,000 |
| 97.5% | 222,233,500 |
| 98.0% | 233,562,500 |
| 98.5% | 241,523,000 |
| 99% | 256,300,000 |
| 99.5% | 280,500,000 |
Determine the closest estimate of the daily ES at the 96.5% confidence level:
A
USD 203,205,500
B
USD 240,924,000
C
USD 280,500,000
D
USD 235,535,643