Z-Score explained

Statistics

What Z-Score measures

Z-Score measures how many standard deviations the current price is from its moving average. A Z-Score of +2 means price is 2 standard deviations above the mean — statistically unusual. Z-Score normalises price deviation across different assets and periods, making it easier to compare setups across a watchlist.

How Z-Score readings are interpreted

Z-Score near zero means price is near its statistical mean. +2 or higher means it's unusually high; -2 or lower means unusually low. These extreme readings occur about 5% of the time in normally distributed data. Z-Score is particularly useful for mean-reversion strategies and identifying overextension.

Conventional Z-Score levels

+2.0 or above: statistically overbought — mean reversion likely
-2.0 or below: statistically oversold — mean reversion likely
+1.0 to +2.0: elevated but not extreme
0: exactly at the mean
Sustained extremes (>+2 for many bars): strong trend or structural break

Where Z-Score works, and where it does not

Z-Score is most powerful for mean-reversion strategies in ranging markets. In trending markets, Z-Score can stay extreme for extended periods as price moves away from the mean — extreme Z-Scores are not conventionally read as reversals in a trend without a trend filter.

Indicators commonly read alongside Z-Score

Bollinger Bands: Z-Score and BB are mathematically related — BB width represents the standard deviation used in Z-Score
RSI: Z-Score extreme + RSI extreme = double confirmation of overextension
ADX: Only use Z-Score for mean-reversion when ADX < 20 (ranging)

Known limitations of Z-Score

Assumes normally distributed returns — financial markets are fat-tailed, so +2σ events happen more often than statistics predict
During trend breakouts, Z-Score gives persistent false 'overbought' signals
Less intuitive for beginners than RSI/Stochastic

Z-Score in practice

In screening, a Z-Score between -1 and -2 within a confirmed uptrend is the configuration conventionally described as a pullback
Pairs approaches take opposing positions in the low and high Z-Score assets within the same sector
Comparing Z-Scores across correlated assets is a standard relative-value technique
A reading sustained above +2.5 for five or more bars indicates trend rather than deviation, which conventionally invalidates a mean-reversion premise

Other statistical measures

Standard Deviation
Kurtosis
Skewness
Entropy

Testing ideas built on Z-Score

A reading of Z-Score can be written as an exact rule and checked against historical data — as a full strategy with entries, exits and costs, or as a single condition and what followed it:

How to backtest a trading strategy without code
Event analysis: what follows a market event

Plot it yourself. Add this indicator to a chart, change every parameter and watch the line move, then backtest how the rule would have behaved on historical data — free on the S&P 500 ETF, no card.

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This is reference material, not advice. It describes what each indicator measures and how its readings are conventionally interpreted. Nothing here is a recommendation to buy or sell anything, and no indicator predicts future prices. GU Analyser is an analytical tool — no money is ever traded here.