|
PureBytes Links
Trading Reference Links
|
> I messed around with this StdDev of individual trade
> returns stuff about 2 years ago. I was unable to do it
> without using an array to store the individual trade
> results, so I was skeptical when you claimed success
> w/ no arrays.
>
> So I plugged your math into an old piece of system
> stat exporter code I wrote awhile back, and lo &
> behold, it does indeed match the results calculated in
> Excel. Now I wish I'd paid better attention in math class.
Heh. I sort of remembered there was a way to do it, so I juggled
equations and tested in Excel until I figured it out.
I started with the basic root-mean-square definition of SD that
subtracts the average from each value of X, so it does indeed
require arrays. (You have to store all the X values, calculate
the average, and then subtract the average from the X values.)
SD = sqrt( sum((Xn - Avg)^2) / (Length-1) )
(Or you might divide by Length; that's apparently a detail that
statisticians argue about.)
Then we start the hocus-pocus:
(Xn - Avg)^2 = Xn^2 - 2*Xn*Avg + Avg^2
If you sum up that value for all Xn's, you get
sum(Xn^2) - 2*sum(Xn)*Avg + Length*Avg^2
So you just accumulate SumX and SumX2 as I did in my code. Then,
since Avg = SumX / Length, the equation turns into
sumX2 - 2*SumX*(SumX/Length)
+ Length*(SumX/Length)*(SumX/Length)
= sumX2 - 2*SumX^2/Length + SumX^2/Length
= SumX2 - SumX^2/Length
...so SD = sqrt( (SumX2 - SumX^2/Length) / (Length-1) )
No arrays required. Now who's gonna buy the prof a beer?? :-)
Gary
|