According to finance theory, the risk of a finacial asset is estimated by the standard deviation the weighted average of the assets expected return.
For the sake of simplicity let us assume that there are only 10 possiblities with equal probability. That means that the difference between each possibility and the expected rate of return is to be squared and then multiplied with the likelihood of its occurence, in this case 0.1 for all the possiblities.
The ten results will then be added together. The square root of the result of this addition will then be the assets standard deviation.
In this particular case, with all the possiblities having the same likelihood of occurence, this is the mathematical equvialent of squaring those same difference as we began with, adding them together and divide the result with the number of possiblities. The square root of the last addition will be the same as in the first example i.e the assets standard deviation.
Finace theory describe a similiar approach to the last method when calculating an assets standard devaition based on the return of the asset for a specific time range -as opposed to an estimated probability distribution- say for the last 10 years. Only difference is that the added squares should now be divided by
one less the number of entries, in this case 9. Why?
Meant to post this in GQ, didn’t ya?
Anyway, the old estimator for standard deviation is a biased estimator, meaning that its expected value isn’t actually the true standard deviation. Replacing 1/n with 1/(n - 1) solves that quite handily.
Yeah, well Kerry would divide it by 1/(n-2) and Bush keeps saying that no “deviation” is standard-- that it’s just a sly way for the Democratics to promote gay marriage.
Just trying to keep the debate going… 
[Moderator Hat ON]
I think this will do better in General Questions.
[Moderator Hat OFF]
Been a while since I did this… hope I remember this correctly.
The difference between the two cases is
looking at known historical past is a definite population
looking at unknown futures, that you are effectively taking a sample from, is estimating a sample.
Samples of populations have different calculations than the populations themselves.
If it helps, pull out a stats 101 textbook that is clearly written (if you can find one), and look up degrees of freedom.