Pairs trading explained simply

What this page is for

Pairs trading sounds exotic but the core idea is simple: two things that normally move together have drifted apart, and you bet they snap back. This page explains the spread, the z-score that signals an entry, why the trade is market-neutral, and the big risk — the pair breaking. Then you can size a trade on the pairs trading calculator.

How it works (the formula)

Take two assets that historically move together — often two companies in the same sector. You track the gap between their prices and normalize it:

The z-score just says how many standard deviations the gap is from its normal level. The usual playbook:

• Entry: when the spread stretches to about z = +2 or −2, take the mean-reversion bet. If A has become expensive relative to B (z high), you short A and buy B, sized to the hedge ratio (β units of B per unit of A).
• Exit: when the spread returns to normal (z back near 0), close both legs for the convergence profit.
• Stop: if the spread keeps stretching past about z = +3, the relationship may have broken — cut it.

Because the long leg is hedged against the short leg in the ratio β, a rally or sell-off that lifts or drops both names largely cancels out. What's left is the spread — which is what you actually bet on.

Inputs and assumptions

• The two assets are genuinely linked (cointegrated), not just briefly correlated.
• A lookback window for the average spread and its standard deviation.
• The hedge ratio β that sets how many units of B offset one unit of A.
• Entry and exit z thresholds, plus a stop for when the link breaks.
• You can actually borrow the short leg, and financing/borrow cost is acceptable.

Worked example 1 — a clean convergence

Two stocks A and B that trade nearly one-for-one, so β = 1. Over the last 60 days the spread (A − B) averaged $2.00 with a standard deviation of $0.50. Today A = $104, B = $101, so the spread is $3.00 — that's z = ($3.00 − $2.00) ÷ $0.50 = +2.0. A looks rich versus B, so you short 1 share of A and buy 1 share of B (hedge ratio 1 — one share against one share; all P&L below is per share).

A week later the spread reverts to its $2.00 average. Watch that the profit is the same regardless of direction:

• Both drift down: A $104→$100 (short gains $4), B $101→$98 (long loses $3). Net +$1 per share.
• Both drift up: A $104→$105 (short loses $1), B $101→$103 (long gains $2). Net +$1 per share.

Either way you make the $1.00 the spread narrowed by ($3.00 down to $2.00). You never needed the market to go anywhere.

Worked example 2 — when the pair breaks

Same entry: short A at $104, long B at $101, spread $3.00, z = +2. But this time the mean-reversion bet is wrong — A gets a surprise upgrade and keeps climbing while B stalls.

• A runs to $112, B ticks to $101.50. The spread has widened to $112 − $101.50 = $10.50, or z = ($10.50 − $2.00) ÷ $0.50 = +17 — the relationship has clearly broken.
• Mark-to-market: short A loses $112 − $104 = −$8; long B gains $101.50 − $101 = +$0.50. Net −$7.50 per share and still bleeding.
• A stop at z = +3 (spread $3.50) would have closed the trade after only about $0.50 of adverse move per share, instead of $7.50.

This is the whole risk of pairs trading in one example: it is not arbitrage. When a real event decouples the two names, the spread can run against you indefinitely, which is exactly why a stop matters.

Common mistakes

• Treating it as risk-free arbitrage. It's a bet that a statistical relationship holds — and relationships break.
• Using correlation instead of cointegration. Two names can be highly correlated while their spread quietly drifts and never reverts.
• Trading without a stop. Mean reversion has no built-in floor; a takeover bid or earnings shock can widen the spread without limit.
• Not sizing the legs to the hedge ratio. Mismatched legs turn a market-neutral trade into a directional one you didn't mean to take.
• Ignoring borrow and financing costs on the short leg, which quietly eat a thin convergence edge.

Methodology & limitations

The definitions and formulas on this page are standard, widely used ways to describe these concepts; every worked-example number is computed by hand from the formula shown so you can reproduce it. Where a rule varies by provider (prop-firm limits especially), we say so — treat the specifics as illustrative, not as any one firm's rulebook.

Not financial advice. This page explains a concept for education only. It is not investment, trading, or financial advice, and no example is a recommendation. Every prop firm writes its own rules and changes them — always verify against your own program, broker, or account terms before acting.

Last updated 2026-07-06.