Question

Your portfolio has a one-day Value at Risk of $55,000 at the 95% level. What is the six- day Value at Risk at the 99% level. ? (Round your answer to the nearest dollar) a. $190,244 b. There is insufficient information to answer this question. c. $134,721 d. $77,667

Answer 1

Step-by-step explanation:

To calculate the six-day Value at Risk (VaR) at the 99% level, we need to consider the time horizon and the confidence level.

Assuming that the portfolio's risk follows a normal distribution and is independent and identically distributed over time, we can use the square root of time rule to estimate the six-day VaR. The square root of time rule states that the VaR scales with the square root of the time horizon.

In this case, the one-day VaR is $55,000 at the 95% level. To estimate the six-day VaR at the 99% level, we multiply the one-day VaR by the square root of 6 (sqrt(6)) and adjust for the confidence level.

sqrt(6) ≈ 2.449

99% confidence level corresponds to the Z-score of approximately 2.326 (for a standard normal distribution).

Therefore, the six-day VaR at the 99% level can be calculated as follows:

Six-day VaR = One-day VaR * sqrt(6) * Z-score

Six-day VaR = $55,000 * 2.449 * 2.326 ≈ $308,568

Since none of the given answer choices match the calculated result, it seems that none of the provided options are correct.