Can someone help me out with the reasoning behind the solution: Question: "Assuming a normal distribution, calcualte the VAR: The 95% VAR for an investor with a $10m portfolio where the average annual return is 6% and there is a 5% chance that the value of the portfolio will fall by more than 10% over a year." In the solution we have VAR = (0.06--0.1)*10m = 1.6m I don't quite understand why... I get that if we ignore any return we have VAR_0.95 = 0.1*10m I feel like I'm missing something really basic here! Any help would be great
In this case we are measuring the VaR relative to what we would expect our portfolio to grow to. So, 5% chance of portfolio falling to $9m. We expect portfolio to grow to $10.6m. So VaR = $1.6m.
I think I'm convinced! In terms of the "formula" is this correct? Var_0.95 = mu+ sigma*phi^-1(0.95) mu = 10*0.06 =0.6 and from the question sigma*phi^-1(0.95) = 0.1*10 = 1 (i.e. we are assuming the loss is distributed N(0,sigma)) and Var_0.95 = 0.6+1 = 1.6
