Annualized historical volatility is always calculate with 10-, 20- days time window. I don't quite understand.
Compare with annualized historical return, annualized historical return is never calculated with 10-, 20- days time window. It's simply calculated with a whole year return data. But, in the context of volatility, even a whole year data is at hand, a time window of 10-,20-days is always used.
Compare with moving average, moving average is calculated with a similar time window method. But moving average is not annualized.
Why hist vol is N DAYS ANNUALIZED?
So, the only reason that come to mind is in the context of option trading. N days annualized historical volatility is compared with N days annualized implied volatility in order to find trading opportunities. Is that correct?