Statement #1:“A portfolio’s VaR will be larger when it is measured at a 5 percent probability than when it is measured at a 1 percent probability.” Statement #2:“A portfolio’s VaR will be larger when it is measured over a month than when it is measured over a day. The answer says Statement #1 is incorrect, while statement #2 is correct. I can understand that Statement #1 is incorrect, as the formula VaR = PV *（Return - Z-score*standard deviation）, and we measure the loss as VaR. So VaR is larger when it is measured at a 1 percent probability where the Z-score is larger. But how to use the formula to prove the Statement #2 is correct? For example, Monthly VaR = PV * ( Monthly Return - Z-score * monthly standard deviation); Annual VaR = PV * (12 * Monthly Return - Z-score * 12^0.5 * monthly standard deviation) How to prove the annual VaR is larger than the monthly VaR?

You don’t really need a formula to prove statement #2: a portfolio can lose more value in a month (on average) than it can in a day.

you have answered your own question - what do you think the root 12 does? same applies to daily/monthly - you throw a root 20 or something into the equation.