The standard deviation (or average squared deviation) is a statistical measure of the variability of a historical series, obtained from the square root of a particular measurement of the dispersion of values around a characteristic value (square root of the variance).

The variance is obtained as follows:

Var( x ) = ( x( 1 ) - x )2 + ( x( 2 ) - x )2 + ... + ( x( N ) - x )2  /  N
Therefore the variance is the sum of the squares of the differences of each value of a historical series, with respect to the average value (X), compared to the number of values making up the series; the standard deviation, instead, is the square root of the variance:

Sqm = std = SQRT( Var( x ) )

The standard deviation is of enormous benefit in technical analysis: in fact, in addition to being part of several indicators (it is the basis of the CCI, Commodity Channel Index and the Bollinger Bands, just to name a few), it is also an indicator itself.

In fact, it has been said that in statistics the standard deviation is a measure of the volatility: the comparison of the pattern assumed by this indicator with that of a stock makes it possible to identify possible areas of stopping of a trend and of reversal.

It is very likely, in fact, that a new trend will occur once the standard deviation reaches abnormally low values, just as high volatility will signal the exhaustion of a trend.

It's clear that it will be necessary to "calibrate" the optimal length from the standard deviation, but this will depend on the nature of the stock - which is more or less speculative (like saying that Ford and Apple are volatile in the same way?) - and as always, from the sensitivity of the analyst.

A fairly "universal" measure has been adopted for 20 days, which roughly corresponds to a month.

It's believed that observing the one-month volatility of a stock is quite informative.