bodhisattva

CP, thank you very much for your response !

1. What you meant are :
Acutually (usually) : Yearly SD > monthly SD > weekly SD > daily SD
if the Yearly SD is calculated as : monthly SD x 12^1/2 or weekly SD x 52^1/2 or
daily SD x 250^1/2, the calculated Yearly SD will be lower than the actual yearly SD,
i.e., the calculated yearly SD is an under-estimated one and the calculated Sharpe ratio
will be HIGHER than the actual/real one.
Am I right ?

2. In your example, I think the return in the numerator shall be : (1+r month1)*
(1+r Month 2) * ...(1+r month 12) -1 , since you use "monthly" SD in the denomintor.
What is the monthly SD here ? The SD of a specific single month's return ?
And this will lead to higher Sharpe ratio (than real one) ?
Since sqrt(12) = 3.464 and the annualized yearly return (compounded from monthly
returns) is not necessarily 3.464x greater than the annualized yearly return, therefore,
I think it is not necessarily that the calculated Sharpe ratio will be HIGHER than the
actual/real one. i.e., there is a likelyhood that the the calculated Sharpe ratio will be
LOWER than the actual/real one. But in any case, the calculated Sharpe ratio will be a
distorted one.
Am I correct ?