The total period tested/trained and displayed should be many, many times that lookback parameter
Yes I agree, of course … but in this instance I’m not testing/training anything.
The point of the chart was simply to illustrate that contrary to @tommcginnis comment that “once the look-back is lined up, they will behave nearly identically”, in fact ATR and SD can behave quite differently.
Suppose that …
TraderA employs SD to determine stop placement
TraderB employs ATR to determine stop placement
If both traders hold positions in the S&P 500, then based on the above chart TraderA would currently be moving his stop further away from the market (due to increasing SD), whereas TraderB would be moving his stop closer to the market (due to decreasing ATR).
The chart clearly does not provide any evidence that one is better than the other, it simply shows that they are most certainly not the same.
The problem becomes one of which formula out of infinity to choose? Sometimes a cheap and fast one is enough though. Been through the rabbit hole and complexity is not really helping much.