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Answer: JPY 484 million
The closest estimate of the daily Expected Shortfall (ES) at the 97.5% confidence level is obtained by averaging the Value at Risk (VaR) figures for confidence levels above 97.5%. According to the data provided, the VaR figures for confidence levels 98.0%, 98.5%, and 99.0%, and 99.5% are JPY 451,993,000, JPY 468,763,000, JPY 490,773,000, and JPY 524,663,000, respectively. By calculating the average of these four VaR figures: \[ ES = \frac{(451,993,000 + 468,763,000 + 490,773,000 + 524,663,000)}{4} \] \[ ES = \frac{1,936,192,000}{4} \] \[ ES = JPY 484,048,000 \] This calculation yields an ES of approximately JPY 484 million, which corresponds to option C. This approach is based on the assumption that ES can be estimated as the mean of the VaR values at higher confidence levels, reflecting the average loss expected when the market moves unfavorably beyond the 97.5% confidence level.
Author: LeetQuiz Editorial Team
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In the context of a wealth management firm that oversees assets amounting to JPY 86 billion, determine the closest approximation to the daily Expected Shortfall (ES) at a 97.5% confidence level, utilizing the given daily Value at Risk (VaR) values.
A
JPY398million
B
JPY400million
C
JPY 484 million
D
JPY497million