Explanation:
Expected Shortfall (ES) is a coherent risk measure defined as the expected loss given that the loss exceeds the Value-at-Risk (VaR) threshold. It can be approximated using a discrete set of VaR estimates in the tail of the distribution.
To estimate the Expected Shortfall at the 97.5% confidence level using the given data, we compute the average of the VaR estimates uniformly distributed starting at the 97.5% confidence level up to the highest provided level (99.5%):
ES = (VaR_97.5% + VaR_98.0% + VaR_98.5% + VaR_99.0% + VaR_99.5%) / 5 ES = (367,882,500 + 378,412,500 + 392,452,500 + 410,880,000 + 439,252,500) / 5 ES = 1,988,880,000 / 5 ES = 397,776,000
This is closest to JPY 398 million. Therefore, Option A is the correct answer.
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| Confidence Level | VaR (JPY) |
|---|---|
| 95.0% | 332,760,000 |
| 95.5% | 336,292,500 |
| 96.0% | 340,095,000 |
| 96.5% | 350,332,500 |
| 97.0% | 359,107,500 |
| 97.5% | 367,882,500 |
| 98.0% | 378,412,500 |
| 98.5% | 392,452,500 |
| 99.0% | 410,880,000 |
| 99.5% | 439,252,500 |
What is the closest estimate of the daily ES at the 97.5% confidence level?
A
JPY 398 million
B
JPY 400 million
C
JPY 405 million
D
JPY 497 million
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