standard deviation using monthly portfolio returns comparing with using daily return, which one has higher standard deviation?

monthly

high frequency data (daily return data) may be prone to asynchronus-ness and thusly put a downward bias on standard deviation and correlatioin.

whats the answer?

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.

Those > signs only hold true if the std dev you calculate is the same for all the measurement periods. If the daily std dev measure happens to be 0.02, but the mothnly ends up being .2 (if the portoflio experiences some large movements on the last day of the month), then the annalized number based on monthly observations is higher, even though itâ€™s only multiplied by sqrt of 12. Make sense?

so if correlation is higher, the standard deviation will be higher given other factors same?