Explanation:
The Expected Shortfall (ES) at a particular confidence level can be approximated as the arithmetic average of the Value at Risk (VaR) estimates at all available confidence levels that are strictly greater than the specified level.
The question asks for the ES at the 96.5% confidence level. Looking at the table, the confidence levels greater than 96.5% are 97.0%, 97.5%, 98.0%, 98.5%, 99.0%, and 99.5%.
The corresponding VaR values are:
We sum these 6 values and divide by 6:
Sum = $211,425,000 + 222,233,500 + 233,562,500 + 241,523,000 + 256,300,000 + 280,500,000 = 1,445,544,000$
Average (ES) =
Thus, the estimated 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
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