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Answer: USD 14.72 million
## Explanation For historical simulation VaR at 99% confidence level with 400 days of data: - The VaR corresponds to the **4th worst loss** (since 1% of 400 = 4) - The returns are ordered from highest to lowest - The 4th worst return is **-1.84%** (counting from the bottom: -1.91%, -1.87%, -1.84%, -1.82%, ...) **Calculation:** - Portfolio value = USD 800 million - VaR = Portfolio value × |4th worst return| - VaR = 800,000,000 × 0.0184 = USD 14,720,000 Therefore, the daily VaR at 99% confidence level is **USD 14.72 million**. **Verification:** - 1st worst: -1.91% → Loss = 15.28 million - 2nd worst: -1.87% → Loss = 14.96 million - 3rd worst: -1.84% → Loss = 14.72 million - 4th worst: -1.82% → Loss = 14.56 million Since we need the 4th worst loss for 99% VaR, the correct answer is -1.84% which gives USD 14.72 million.
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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
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