This question in part (ii) asks for a VaR to be calculated based on a Normal distribution. The solution does the standard approach of finding out what t equates P(Z < (t-mu)/sigma) = Phi(-2.3263) = 0.01 But then this t (or rather, -t) is not the VaR. Is this because the question says "relative to the expected value"? Hence we take t away from the expected value of the portfolio already calculated? If it did not have this "relative to" qualification, t would be the VaR (the "usual" definition)? One final point to check: would the VaR be the t which came out of (t-mu)/sigma = -2.3263, or would the answer be -t? Thanks Eleanor
It depends whether the random variable denotes a portfolio's value or a portfolio's performance (ie profit or loss). In this case it's the former and that's why it's expressed relative to the expected value. If the random variable represents the profit or loss of a portfolio then the VaR is "-t".
