"Bill Martin" wrote:
As I recall, you're supposed to use the sqrt of the number
of days of data you've used to annualize it -- not simply the
sqrt(250). In the example you cited it would be sqrt(21).

I disagree. You scale based on the relationship between the
units of time, not the sample size.

If you have a daily volatility, you scale by 21 for to get monthly
volatility and by 252 to get annual volatility.

It has nothing to do with how many days -- the sample size
-- that you used to determine daily volatility. Of course, the
computation of the daily volatility statistic -- standard deviation
-- depends on the number of days (data points) in the sample.
But not how you subsequently annualize it.

Example references, none of which mention sample size in
determining the scale factor:

http://en.wikipedia.org/wiki/Historical_volatility
http://www.riskglossary.com/link/volatility.htm
http://www.riskmetrics.com/courses/m...risk/time.html

Also you're supposed to *divide* by the sqrt(time period), not
*multiply* by it which makes quite a difference.

I disagree. You divide by the sqrt of time as a __fraction__ of
a year to convert a shorter-period volatility to annual volatility.
Conversely, you multiply by the sqrt of time as a __fraction__
of a year to convert annual volatility to a shorter-period volatility.

But operative word is "fraction". Those rules are the same as
multiplying by the sqrt of time in units per year and dividing by
the sqrt of time in units per year, respectively.

This is confirmed by the Wikipedia article you cite, as well as
the additional articles I cite above. Using the Wikipedia examples ....

To convert daily volatility (vd) to annual volatility (va): va =
vd / sqrt(1/252). That is the same as va = vd*sqrt(252).
Proof:

va^2 = vd^2 / (1/252) = 252 * vd^2
va = vd * sqrt(252)

Conversely, to convert annual volatility (va) to monthly volatility
(vm): vm = va * sqrt(1/12). That is the same as vm =
va / sqrt(12). Proof:

vm^2 = va^2 * (1/12) = va^2 / 12
vm = va / sqrt(12)