Let's say you want to calculate (estimate) the stdev of returns (or vol) over 10 days, name it vol10. You know the vol for each day, say Day1 - s1, Day2 - s2 and so on to Day10 with vol s10."am i going to use 10 day returns or stdev of 1 day returns rescaled by the root of time.". i don't know the difference .. whats the difference. [/B]
You cannot add vols but you can add variances i.e. the square of vol
vol10= SQRT(Var10) = SQRT(s1^2+s2^2+...+s10^2)
Another way to do it is to take a daily vol value, say the most recent one Day1 -> s1 and "convert" it form daily to 10-day value.
vol10=SQRT(Var10)=SQRT(10*s1^2) which is SQRT(10)*s1
A more familiar example is when you convert daily vol to annual vol. You multiply with SQRT(252)~16 assuming 1 year has 252 wdays