Financial Risk Manager Part 1
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A newly employed quantitative analyst at a financial firm was tasked by a portfolio manager to compute the Value at Risk (VaR) for 10-, 15-, 20-, and 25-day horizons. It is known that the annualized volatilities of the daily returns for these periods are the same, and the daily returns follow a normal distribution with identical and independent increments, having a zero mean. Considering this information, which of the following VaR estimates for the portfolio is not consistent with the others?
A newly employed quantitative analyst at a financial firm was tasked by a portfolio manager to compute the Value at Risk (VaR) for 10-, 15-, 20-, and 25-day horizons. It is known that the annualized volatilities of the daily returns for these periods are the same, and the daily returns follow a normal distribution with identical and independent increments, having a zero mean. Considering this information, which of the following VaR estimates for the portfolio is not consistent with the others?
Explanation:
The explanation provided in the file content indicates that the correct answer is B, VaR(15-day) = USD 503 million, because it is inconsistent with the other VaR estimates. The inconsistency arises from the calculation of the VaR(1-day) values derived from each option:
- For option A, VaR(10-day) = USD 474 million, which when divided by the square root of 10 (since the time period is 10 days), gives VaR(1-day) = 150 million.
- For option B, VaR(15-day) = USD 503 million, divided by the square root of 15, results in VaR(1-day) = 130 million.
- For option C, VaR(20-day) = USD 671 million, divided by the square root of 20, gives VaR(1-day) = 150 million.
- For option D, VaR(25-day) = USD 750 million, divided by the square root of 25, results in VaR(1-day) = 150 million.
The calculations show that the VaR(1-day) values for the 10-day, 20-day, and 25-day periods are consistent at 150 million, while the 15-day period's VaR(1-day) is 130 million, making option B the outlier and the incorrect estimate according to the given conditions. The annualized volatilities of daily returns for the different periods are assumed to be equal, and daily returns are normally distributed with a mean of zero, which implies that the VaR estimates should scale consistently with the square root of time for each period.