A same-session pair book with a morning-fixed volatility envelope

A two-name market-neutral book

Pairs-trading, in this write-up, is a market-neutral book that opens a long in one stock and a short in a related stock together, so the wager is on relative displacement rather than on market direction. The two legs are opened at the same time on the premise that a temporary decorrelation later mean-reverts.

Mean-reversion is the working assumption that two names that usually travel together will, after a temporary breakdown in co-movement, pull a normalized spread back toward its typical level.

The book is specified for highly correlated pairs with a correlation-coefficient of at least 0.5, where plus one means tandem movement and minus one means opposite movement.

Reading the live spread

The normalized-spread is the live relative-value line formed by scaling each stock's last price by its prior close and subtracting those two ratios. The live spread is last price of the first name over its prior close, minus last price of the second name over its prior close.

Envelopes fixed at the session open

Bollinger-bands are used here as a pair-level volatility envelope, computed at the open from each name's historical volatility and their correlation, and used as the quantitative baseline the live spread must breach and then recross. Upper and lower volatility envelopes are computed at the start of the session. A move to the upper envelope treats the first name as rich versus the second, and a move to the lower envelope treats the first name as cheap.

Historical-volatility is a lookback standard deviation of close-to-close percentage change, typically read over thirty sessions and treated as an input to the daily pair envelope. A 20-dollar name with a 20 percent reading is described as spending about 68 percent of that window between 16 and 24 dollars under a normal curve.

A one-day pair envelope is formed from the two 30-day volatilities, a 252-session year scale of 0.063, and one minus the pair correlation. Volatilities of 0.57 and 0.70 with correlation 0.60 produce a one-sigma band of 0.032.

The volatility-factor is a multiplier, defaulted to one and a half standard deviations, that turns the daily pair envelope into the entry threshold and a still-wider stop. The default signal uses 1.5 standard deviations, stated as giving prices at least an 80 percent chance of reverting toward the mean, which turns the 0.032 one-sigma band into 0.048.

Entry after a recross

A long-first-name entry waits for the spread to cross back above the lower envelope, then buys the first name one tick above the next bar high and shorts the second name on that fill. The reverse entry waits for a cross below the upper envelope and shorts the first name one tick below the next bar low.

A joint target and stop

Both legs exit together when the spread recrosses zero as the target, or when it extends beyond the volatility factor times the envelope as the stop.

Liquidity, pairing and news

Operational constraints in the write-up include screening for liquidity and volatility, preferring same-industry leader-laggard pairings, opening the short leg first when an uptick constraint applies, and standing aside after significant news until the spread begins to revert.

A leader-laggard-pair is a same-industry pairing of a faster growth name against a slower value or blue-chip name so the spread can travel even when both prices move in the same direction.