Glossary term
Z-Score
Standard deviations from the mean: (x minus mu) divided by sigma. Tells you how extreme an observation is relative to its own history. +/- 2 sigma covers ~95% of normal observations, +/- 3 sigma ~99.7%. Closelook's Cointegration Monitor opens pair trades at +/- 2 sigma on the spread and exits near Z = 0.
Definition & Context
The Z-Score standardises an observation by expressing it in units of its own standard deviation: Z = (x − μ) / σ. A Z of 0 is the mean; Z = +1 sits one standard deviation above the mean; Z = −2 is two standard deviations below. Under a normal distribution, Z ∈ ±1 covers 68% of observations, ±2 covers 95%, ±3 covers 99.7%. The metric is distribution-agnostic in principle but gains its punch under approximate normality.
Practical caveats: financial returns are not normal. Fat tails mean that observed ±3σ events occur far more often than 0.3% of the time. Using Z-scores on raw returns underestimates tail risk; using them on spreads between cointegrated assets works far better because the spread is often much more mean-reverting than either underlying. Rolling windows matter: a Z computed on 20 days behaves differently from one computed on 250 days.
Why It Matters for Investors
Closelook’s Cointegration Monitor uses Z-scores extensively. Once a pair is identified as cointegrated, the spread is standardised and plotted as a rolling Z. Entries trigger at Z ±2 (statistically extreme deviation from equilibrium); exits at Z near 0 (return to mean); stop-outs at Z beyond ±3 (cointegration has likely broken). The same framework runs in the Pattern Scanner: many of the 51 Directional-Alpha patterns use Z-scores on price-to-moving-average or spread-to-mean deviations as entry triggers.
Related Concepts
Z-Score is the engine under Cointegration pair trading and Linear Regression Channel deviation bands; it is a cousin of the Sharpe Ratio, which standardises risk-adjusted return.