Z-Scores & Bands

Every pair on the terminal carries a set of z-space levels. This page defines exactly what they mean.

The z-score

The spread for a pair A-B is:

spread = price_A − β · price_B

The z-score standardizes it:

z = (spread − μ) / σ

where β (hedge ratio), μ (spread mean), and σ (spread volatility) are fitted daily on historical data. During the day, the live z-score ticks in real time — live prices measured against that day's locked statistics.

The bands

Entry — the |z| level at which the stretch is considered tradeable. Below entry the pair is forming; beyond it the pair is past its entry band.
Exit — measured as travel from the entry threshold, not a fixed z-level. A trade entered short at +2.0σ with an exit of 1.5 targets z = +0.5; the equivalent long entered at −2.0σ targets −0.5. Exits may overshoot the mean.
Stop — the |z| level at which the divergence is treated as a broken relationship rather than an opportunity.
Timeout — a maximum holding period; mean reversion that hasn't happened within the window is treated as a failed thesis.

Two clocks

The terminal deliberately runs on two clocks:

Daily — β, μ, σ, and all band levels are refit once per day and locked.
Live — the z-score updates in real time against those locked numbers.

This means an intraday z reading is always interpretable: it is today's prices measured against a fixed, stated ruler — never a moving target.

The z-score

The spread for a pair A-B is:

spread = price_A − β · price_B

The z-score standardizes it:

z = (spread − μ) / σ

The bands

Entry — the |z| level at which the stretch is considered tradeable. Below entry the pair is forming; beyond it the pair is past its entry band.

Exit — measured as travel from the entry threshold, not a fixed z-level. A trade entered short at +2.0σ with an exit of 1.5 targets z = +0.5; the equivalent long entered at −2.0σ targets −0.5. Exits may overshoot the mean.

Stop — the |z| level at which the divergence is treated as a broken relationship rather than an opportunity.

Timeout — a maximum holding period; mean reversion that hasn't happened within the window is treated as a failed thesis.

Two clocks

The terminal deliberately runs on two clocks:

Daily — β, μ, σ, and all band levels are refit once per day and locked.

Live — the z-score updates in real time against those locked numbers.

This means an intraday z reading is always interpretable: it is today's prices measured against a fixed, stated ruler — never a moving target.