Financial Risk Manager Part 1

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Explanation:

The explanation provided in the file content indicates that the correct answer is B, which is identified as inconsistent with the other VaR estimates. The inconsistency arises from the calculation of the Value at Risk (VaR) for a 1-day period based on the provided VaR for different time periods. The calculations are as follows:

For a 10-day period, the VaR is USD 474 million. Dividing this by 10 gives a 1-day VaR of USD 150 million.
For a 15-day period, the VaR is USD 503 million. Dividing this by 15 results in a 1-day VaR of USD 130 million, which is different from the 1-day VaR calculated for the other periods.
For a 20-day period, the VaR is USD 671 million. Dividing this by 20 gives a 1-day VaR of USD 150 million.
For a 25-day period, the VaR is USD 750 million. Dividing this by 25 results in a 1-day VaR of USD 150 million.

Since the daily returns are assumed to be independently and identically normally distributed with a mean of zero and equal annualized volatilities, the 1-day VaR should be consistent across different time periods. The only exception is the 15-day VaR, which yields a different 1-day VaR compared to the other periods. This inconsistency makes option B the correct answer.

Explanation:

For a 10-day period, the VaR is USD 474 million. Dividing this by 10 gives a 1-day VaR of USD 150 million.
For a 15-day period, the VaR is USD 503 million. Dividing this by 15 results in a 1-day VaR of USD 130 million, which is different from the 1-day VaR calculated for the other periods.
For a 20-day period, the VaR is USD 671 million. Dividing this by 20 gives a 1-day VaR of USD 150 million.
For a 25-day period, the VaR is USD 750 million. Dividing this by 25 results in a 1-day VaR of USD 150 million.

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A newly hired quantitative analyst at a financial firm is assigned by a portfolio manager to calculate the Value at Risk (VaR) for a portfolio over 10-day, 15-day, 20-day, and 25-day periods. The portfolio manager, however, notices an inconsistency in the analyst's results. The context provided specifies that the annualized volatilities for the daily returns over these time horizons are equal. The daily returns are also assumed to be normally distributed, independent, and have a mean of zero. Based on this information, determine which of the following VaR figures for the portfolio is inconsistent with the others?

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Last updated: February 6, 2026 at 14:03

VaR(10-day) = USD 474 million

14.4%

VaR(15-day) = USD 503 million

58.5%

VaR(20-day) = USD 671 million

17.8%

VaR(25-day) = USD 750 million

9.3%