Converting return and stdev from monthly to weekly

Hi, in one of the problems in the text involving VAR calculation, the solution elects to convert monthly return and standard deviation by first annualizing it (*12, or *sqrt(12) for stdev). Then divided by 52 (or sqrt(52)). Is there a reason it’s done this way instead of simply divided by 4 assuming there are four weeks in a month? Is this the “standard” way to convert monthly returns to weekly ones?

Due to the fraction; if you assume 12 months and 4 weeks each then it must be 48 weeks. But we use 52 weeks for annual. FOR Ex. Monthly SD = 2.76% if you take direct weekly : 2.76 / sqrt(4) = 1.380% the same thing 2.76% * sqrt(12) / sqrt(52) = 1.326% If you want to reconcile : 48/52 =0.923077 if you multiply 1.380% * sqrt(0.923077) it matches with 1.326% ! In short, to use 52 weeks instead of 48 weeks, that was calculated that way !!

Thanks FRM. I guess I’ll do it the way it’s done in the text.