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Answer: USD 14.56 million
## Explanation **Historical Simulation Method for VaR**: - **Portfolio value**: USD 800 million - **Number of observations**: 400 days - **Confidence level**: 99% **Calculation**: \[ \text{Observation number} = (1 - \text{confidence level}) \times \text{total observations} \] \[ \text{Observation number} = (1 - 0.99) \times 400 = 4 \] This means we need the 4th worst loss from the ordered returns. From the given returns (ordered from highest to lowest), the worst returns are: - -1.91% (worst) - -1.87% (2nd worst) - -1.84% (3rd worst) - -1.82% (4th worst) **VaR calculation**: \[ \text{VaR} = \text{Portfolio value} \times \text{4th worst return} \] \[ \text{VaR} = 800,000,000 \times 0.0182 = 14,560,000 \] Therefore, the 99% VaR is **USD 14.56 million** **Note**: The 4th worst return is -1.82%, not -1.76% which appears earlier in the sequence.
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Rational Investment Inc. is estimating a daily VaR for its fixed income portfolio currently valued at USD 800 million. Using returns for the last 400 days (ordered in decreasing order, from highest daily return to lowest daily return), the daily returns are the following: 1.99%, 1.89% 1.88% 1.87% ......, -1.76%, -1.82%, -1.84%, -1.87%, -1.91%
At the 99% confidence level, what is your estimate of the daily VaR using the historical simulation method?
A
USD 14.08 million
B
USD 14.56 million
C
USD 14.72 million
D
USD 15.04 million