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Answer: JPY 484 million
**Explanation:** Expected Shortfall (ES) at the 97.5% confidence level is calculated by taking the average of the VaRs for all confidence levels greater than 97.5%. From the table, the VaR values above 97.5% confidence level are: - 98.0%: JPY 451,993,000 - 98.5%: JPY 468,763,000 - 99.0%: JPY 490,773,000 - 99.5%: JPY 524,663,000 Calculation: ES = (451,993,000 + 468,763,000 + 490,773,000 + 524,663,000) / 4 ES = 1,936,192,000 / 4 ES = JPY 484,048,000 This rounds to approximately JPY 484 million, which matches option C. **Key Concept:** Expected Shortfall (ES) represents the average loss in the worst (1-confidence level)% of cases, providing a more comprehensive risk measure than VaR as it captures the tail risk beyond the VaR threshold.
Author: LeetQuiz .
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A wealth management firm has JPY 86 billion in assets under management. The portfolio manager computes the daily VaR at various confidence levels as follows:
| Confidence Level | VaR (JPY) |
|---|---|
| 95.0% | 397,463,000 |
| 95.5% | 401,682,500 |
| 96.0% | 406,224,500 |
| 96.5% | 418,453,000 |
| 97.0% | 428,934,000 |
| 97.5% | 439,415,500 |
| 98.0% | 451,993,000 |
| 98.5% | 468,763,000 |
| 99.0% | 490,773,000 |
| 99.5% | 524,663,000 |
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 484 million
D
JPY 497 million