Converting return and stdev from monthly to weekly

[creperie]

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?

 

[FRM2cfa]

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 !!

 

[creperie]

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