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Financial Risk Manager Part 2

Financial Risk Manager Part 2

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In the context of financial risk management, Expected Shortfall (ES), also known as Conditional Value at Risk (CVaR), is a risk measure that evaluates the potential extreme losses in a portfolio or investment. ES is particularly useful because it takes into account the severity of losses beyond the Value at Risk (VaR) threshold. Given this, what would be the closest estimate of the daily Expected Shortfall (ES) with a 97.5% confidence level?

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Explanation:

The expected shortfall (ES) is an estimate of the potential loss that can be expected to be exceeded with a certain confidence level. In this case, the ES at the 97.5% confidence level is calculated by taking the average of the Value at Risk (VaR) values at confidence levels greater than 97.5%. The VaR values provided for the 98.0%, 98.5%, 99.0%, and 99.5% confidence levels are used for this calculation. The formula for the ES is:

ES=VaR98.0%+VaR98.5%+VaR99.0%+VaR99.5%4ES = \frac{VaR_{98.0\%} + VaR_{98.5\%} + VaR_{99.0\%} + VaR_{99.5\%}}{4}ES=4VaR98.0%​+VaR98.5%​+VaR99.0%​+VaR99.5%​​

Plugging in the values from the file content:

ES=378,412,500+392,452,500+410,880,000+439,252,5004ES = \frac{378,412,500 + 392,452,500 + 410,880,000 + 439,252,500}{4}ES=4378,412,500+392,452,500+410,880,000+439,252,500​

ES=1,630,995,5004ES = \frac{1,630,995,500}{4}ES=41,630,995,500​

ES=407,748,875ES = 407,748,875ES=407,748,875

However, the closest estimate given in the options is JPY 405 million, which corresponds to option C. This discrepancy could be due to rounding differences in the calculation or presentation of the final answer. The correct calculation method is to average the VaRs at higher confidence levels, and the closest match to the calculated ES is option C, JPY 405 million.

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