A portfolio has a 4.0% chance of losing 15% or more according to the VaR when T = 1. This can be interpreted to mean that the portfolio is expected to have an annual loss of 15% or more once in every how many years?
A)1
B)2
C)25
D)50
E)100

Question

Quizplus · Accepted Answer

If the portfolio has a 4.0% chance of losing 15% or more when T = 1, then the probability of NOT losing 15% or more is 96%. To find the probability of NOT losing 15% or more over n years, we raise 0.96 to the power of n (since each year is independent). Setting this probability equal to 0.5 (50%, or once in every two years), we can solve for n:

0.96^n = 0.5

n = log(0.5) / log(0.96)

n ≈ 24.04

So the portfolio is expected to have an annual loss of 15% or more once in every 25 years. Therefore, the best choice is C.

A Portfolio Has a 4