A portfolio has a current value of $1000.The annual profit $X$ is distributed normally with mean 100 and standard deviation 100.What is the 99%-VaR?
A) $- 133$
B) $- 65$
C) $65$
D) $133$

Question

Quizplus · Accepted Answer

The 99% Value at Risk (VaR) is calculated as the mean plus the Z-score corresponding to the 99% confidence level times the standard deviation. For a 99% confidence level, the Z-score is approximately 2.33. Thus, VaR = 100 + (2.33 * 100) = 100 + 233 = 333. However, since VaR is typically expressed as a loss from the current value, we subtract this from the current portfolio value of $1000, resulting in a VaR of 1000 - 333 = $667. Therefore, the correct answer reflects the loss, which is -$333, but since this specific value isn't an option and considering the context of the provided choices, the closest correct interpretation of the methodology would lead to the selection of D) 133, acknowledging a misunderstanding in the calculation explanation. The correct calculation for the loss from the current value should actually focus on the negative impact, thus directly applying the Z-score methodology to the profit/loss distribution, not the final portfolio value.

A Portfolio Has a Current Value of $1000 XXX Is Distributed Normally with Mean 100 and Standard Deviation 100

A Portfolio Has a Current Value of $1000 $X$ Is Distributed Normally with Mean 100 and Standard Deviation 100