CFAI Book 5 pg 111 says that:
"A 5% VAR would be equal to the expected monthly portfolio return minus 1.65 × (monthly portfolio standard deviation), or –VAR = μp – 1.65σp. The increase in expected return would result in a lower calculated VAR (smaller losses).
I tried to put numbers in the formula and tried to calculate VAR and had opposite results. Can anybody explain?
My advise will be to think about it logically. Greater return leads to lower losses (lower VAR)
Regarding the formula to calculate VAR, you are just considering the expected return.
Increases in expected returns are associated with increasing standard deviation, think it that way.
Respectfully I would disagree with the last comment of your answer. In this context, increase in expected return does not have to increase the std. What I believe they are pointing out is that your starting point for calculating VAR is the expected return. The 1.65std away will be moved up in value by the amount of your increased expected return. On the other side your 5% significance level will be higher in the upside as well. Think about a number line with a normal curve centered around an expected return. If you shift this curve to the right, all the significant points will increase by the same amount leaving the std. constant. Thats how I interpret that statement.