Standard-Deviation Extension (z-score stretch)
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Definition
Standard-deviation extension is a z-score that measures how far price has stretched from a reference mean (e.g. a moving average) in units of standard deviation, quantifying how statistically overextended a move is and flagging mean-reversion ('snap-back') candidates.
How to read it
z = (price - mean) / standard deviation. A reading of +2 means price is two standard deviations above its mean (stretched high / potentially overbought); -2 is two SD below (stretched low). Roughly speaking, larger absolute z-scores are rarer and imply greater odds of at least a short-term reversion toward the mean. This is the statistical engine behind Bollinger %B - a +2 stretch corresponds to price at the upper 2-sigma band. Extreme readings mark 'stretched' or 'snap-back candidate' conditions.
How practitioners use it
Used as context among multiple indicators — never as a standalone signal to act.
Less common professional uses
Fading a high z-score in a strong trend is the classic failure mode: in a trend price can stay 2-3 SD stretched or push further ('a stretched market can get more stretched'). Gate reversion trades with a range/regime filter (ADX low) before fading. z-scores assume an approximately stable mean and normal distribution; financial returns are fat-tailed and the mean drifts, so a 3-sigma event is far more common than the normal model predicts - never size as if extreme z guarantees reversion. The lookback for mean and SD dictates everything; a short window makes almost everything look stretched and a long one hides it. Fix a principled window and beware optimizing it to fit past snap-backs (curve-fitting).
Sources & provenance
Statistical mean-reversion practice; underpins Bollinger %B
This page is educational content published by Pachira Aquatica Global LLC. It is not investment advice and not a recommendation.