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Answer: JPY 405 million
**Correct Answer:** C **Explanation:** C is correct. An estimate of the expected shortfall (ES) can be obtained by taking the average of the VaRs for the various confidence levels that are greater than 97.5%. Therefore, ES = (378,412,500 + 392,452,500 + 410,880,000 + 439,252,500) / 4 = JPY 405,249,375 **Section:** Market Risk Measurement and Management **Learning Objective:** Estimate the expected shortfall given profit and loss (P/L) or return data. **Reference:** Kevin Dowd, Measuring Market Risk, 2nd Edition (West Sussex, England: John Wiley & Sons, 2005). Chapter 3 - Estimating Market Risk Measures: An Introduction and Overview
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A wealth management firm has JPY 72 billion in assets under management. A portfolio manager at the firm estimates the daily VaR at various confidence levels as follows:
| 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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