profil

I am not sure if the question is being asked correctly.
I think question asked is - if monthly returns are presented - a monthly std deviation is found and then moved up to a annual std deviation - annual Std dev from monthly = monthly std dev * sqrt(12)
annual std deviation from daily = daily std dev * sqrt (250)
annualized std deviation from daily  annualized std deviation from weekly  annualized std dev from monthly  annual std dev.
Lengthening measurement interval - reduces the Std Deviation - and thus Sharpe Ratio can be gamed.