In Chapter 4 Page 147, I see that it asked to find 97.5% VaR. We basically calculate Pr(X<t) = 0.025 and get t = -7.68%. Then according to the definition in the book VaR(X) = -t where Pr(X<t)=p, we get VaR = 200m * (7.68) = 15.36 I observe a similar question in 2021 April CM2 Exam. A person has 800 to invest, with rate of return ~Norm(7%,5.5%^2). It asked us to calculate the 99.5%VaR. If we follow our core reading definition/example, we should get Pr(X<t) = 0.05, we should get t=-7.1669%. Then we should get VaR(X) = 800 * 7.1669%. i.e. we are 99.5% certain that we will not loss more than 57.34 over the next year. However in the solution, instead of 800*7.1669%, it is using 800*(1-7.1669%). I wonder which definition (the book method in p.147 or the IFOA solution) is correct.
Whilst it is true that the examiners would also have accepted 800*(1-7.1669%), this alternative does not match with the definition of VaR in the Core Reading, nor does it reflect the true purpose of a risk measure. This alternative answer would allow us to be 99.5% sure that the portfolio won’t lose more than of its value over the next year, which isn’t a lot of help to a risk manager. My advice would be to work on the assumption that the 57.34 is correct and that the "alternative solution" will not be a solution next time. John
