VAR- monthly from annual

CFAI Volume 5 Risk management EOC Question 19: Annual return, annual sd is given and the question asks for monthly VAR. The correct answer is arrived after converting the annual return and annual sd to monthly values and then computing monthly VAR.

We can also arrive at monthly VAR by first computing the annual VAR right? I mean, use annual return and annual sd to compute annual VAR and then use the formula monthly VAR = annual VAR / sqrt(12). Since the example given in the book is multiple choice quesiton, we can calculate it both ways and choose whichever matches. What if this is part of essay question? Which is the correct method??

Pleasee clarify.

please go ahead and check your formula .

No. they are not mathematically the same and you will get different answers. You cannot calculate monthly VAR = Annual / sqrt(12). That ‘shortcut’ works only when the assumption is that rate of return is 0. If the rate of return is anything other than zero, then you need to calculate return, SD seperately for the monthly time period and use that to calculate VAR. Hope this clarifies.