Answer: VaR(15-day) = USD 503 million

The explanation provided in the file content indicates that the portfolio daily returns are assumed to be independently and identically normally distributed with a mean of zero. The task is to identify which of the given Value at Risk (VaR) calculations for different time periods is inconsistent with the others. The VaR is a statistical measure used to assess the potential loss in value of a portfolio over a specified time period at a given confidence level. Given that the annualized volatilities of daily returns for the four periods are equal, the correct approach to identify the inconsistency is to calculate the VaR for a 1-day period from each of the provided VaR values for the 10-, 15-, 20-, and 25-day periods. This is done by dividing the VaR of each period by the square root of the number of days in that period (since volatility scales with the square root of time). The calculations are as follows: - For a 10-day period, \( VaR(1-day) = \frac{474}{\sqrt{10}} = 150 \) million. - For a 15-day period, \( VaR(1-day) = \frac{503}{\sqrt{15}} = 130 \) million. - For a 20-day period, \( VaR(1-day) = \frac{671}{\sqrt{20}} = 150 \) million. - For a 25-day period, \( VaR(1-day) = \frac{750}{\sqrt{25}} = 150 \) million. Upon comparing these 1-day VaR values, it is clear that the VaR calculated for a 15-day period (130 million) is different from those calculated for the 10-, 20-, and 25-day periods (all 150 million). Therefore, the inconsistent VaR value is the one for the 15-day period, which is option B: VaR(15-day) = USD 503 million.

Author: LeetQuiz Editorial Team