Before re-inventing the wheel: The indicator that you are looking for is called Bollinger's %B.

Standard configuration - as shown - is +/- 2 SD around a 20 period SMA.
Bollinger himself uses a 0/100 scaling instead of 80/20 (because in relation to 2 SDs 80%/20% don't really make much sense).
He just wants to know how much of +/- 2 SDs are maxed out.

You can download it here:

Download: Bollinger PercentB The Bollinger Bands® Percentage B is a technical indicator based upon the Bollinger Bands® study; it plots a histogram showing position of price relative to the bands. It is calculated as percentage ratio of two differences: first one is the difference … persondynoweb

(Default style is bar here, but you can switch it to line - which would be standard.)

The 20-period standard deviation for the data above is 6.787. Note that this is the "full population" version of the Standard Deviation. There is a different kind of Standard Deviation calculation that is used when you are taking a statistical sample of a population, but that version is not used in technical analysis since all of the data points are known.

You are correct in your assumption that all data points are known. However, the data points are not the 20 bar closes that you mention, but all transactions that occured during the period represented by the 20 bar. This clearly shows that you only use a meagre sample of all trades to approximate the standard deviation.

To calculate the correct standard deviation, you should use unfiltered tick data and then calculate the standard deviation from the full population.

But even if you do not have full resolution tick data available, but only have the OHLC and volume data from the last 20 bars, you can do much better than calculating the standard deviation from the closes:

-> first of all you can take into account the volume of each of the 20 bars
-> also the bar close should be replaced with a better price such (open + high + low + close)/4


The chart below shows how a modified calculation of the standard deviation which uses 80 sample points and takes into account volume (blue plot) gives us a better approximation of the population standard deviation than the simple formula based on 20 closes (orange plot).

Thanks Harry,

I've done an advanced search to try and find your anaStdDevBands and have not been successful. Can you provide the link please.

All the best,
John

I have not had the time to put it into Big Mike's downloads. I will send you a link to the indicator via private message.