Z-Score normalizes the distance between price and its rolling mean by the rolling standard deviation. Values are dimensionless and comparable across symbols and timeframes.

Formula

mean = SMA(close, period)
sd   = stddev(close, period)
z    = (close - mean) / sd

Params

period - window for the mean and stddev. Required.

Output

Single column named after your indicator (e.g. zscore).

Common thresholds

| |z| value | Meaning | |---|---| | > 1 | Mildly extended | | > 2 | Statistically rare (~5% tail) | | > 3 | Very rare (~0.3% tail) |

These are based on a normal distribution. Real returns have fatter tails - extreme readings happen more often than the normal would suggest.

Usage

Mean reversion: fade z > 2 and z < -2 back toward zero.
Trend filter: skip trades when |z| < 0.5 (price is uneventfully near the mean).
Cross-symbol portfolio rules: rank multiple symbols by current Z-Score and trade the most extreme.

Pitfalls

The mean and stddev are based on the symbol's recent history - they shift over time. A "Z = 3" reading during a calm period can be very different from a "Z = 3" reading during a panic. Combine with an absolute volatility filter for portability.