Answer: JPY405million

The expected shortfall (ES) is a risk measure that estimates the average loss that could be expected to be exceeded with a certain confidence level, beyond the value-at-risk (VaR). In this scenario, the portfolio manager has provided VaR estimates at various confidence levels. To estimate the ES at the 97.5% confidence level, we take the average of the VaRs for the confidence levels that are greater than 97.5%. The VaRs for the confidence levels 98.0%, 98.5%, 99.0%, and 99.5% are given as JPY 378,412,500, JPY 392,452,500, JPY 410,880,000, and JPY 439,252,500, respectively. To calculate the ES at the 97.5% confidence level, we sum these VaR figures and divide by the number of data points (which is 4 in this case): \[ ES = \frac{(378,412,500 + 392,452,500 + 410,880,000 + 439,252,500)}{4} \] \[ ES = \frac{1,620,995,500}{4} \] \[ ES = JPY 405,248,875 \] The closest estimate of the ES at the 97.5% confidence level is JPY 405 million, which corresponds to option C.

Author: LeetQuiz Editorial Team