The Half-Life of Mean Reversion
Not all cointegrated pairs revert to their mean at the same speed. A pair with a very long half-life might take 60-90 days for the spread to halve from its current deviation. A pair with a short half-life might revert in 5-15 days. The half-life determines the practical tradeability of a pair.
Half-Life of Mean Reversion (Ornstein-Uhlenbeck model):
Spread reversion: dS_t = theta * (mu - S_t) * dt + sigma * dW_t
Where:
theta = mean reversion speed (higher = faster reversion)
mu = long-run mean of the spread
sigma = volatility of the spread
dW_t = Wiener process (random component)
Half-Life = ln(2) / theta
Practical interpretation:
Half-life < 15 days: Excellent tradeable pair (fast reversion)
Half-life 15-30 days: Good tradeable pair
Half-life 30-60 days: Acceptable but requires patience
Half-life > 60 days: Questionable tradeability (capital tied up too long)
Fintiq's Pairs tab calculates and displays the estimated half-life of mean reversion for each pair you enter. This is one of the most important outputs to check before committing to a pairs trade: a pair with strong cointegration (low ADF p-value) but a 90-day half-life is much harder to trade profitably than one with the same cointegration strength but a 12-day half-life.
Classic LSE Pairs with Strong Cointegration History
| Pair | Sector | Economic Link | Typical Half-Life |
|---|
| BP / Shell (SHEL) | Integrated Oil | Oil price, refining margins, ESG transition | 10-20 days |
| Lloyds / Barclays | UK Retail Banking | Bank Rate, UK mortgage market, PRA regulation | 15-25 days |
| Rio Tinto / BHP | Diversified Mining | Iron ore, copper, Australian operations | 12-22 days |
| Whitbread / IHG | Hotels / Hospitality | UK hotel occupancy, RevPAR, consumer spending | 20-35 days |
| Tesco / Sainsbury's | UK Grocery | UK food retail market share, consumer spending | 18-30 days |
Note: the Tesco/Sainsbury's pair was disrupted by Tesco's 2014 accounting scandal, illustrating the structural break risk. Always verify that the economic rationale for a pair remains intact before trading it.
The Z-Score Trading Signal
Once you have confirmed cointegration and checked the half-life, the trading signal is generated from the Z-score of the spread — how many standard deviations the current spread is from its historical mean:
Spread = Price_A - (beta * Price_B)
where beta = hedge ratio from cointegrating regression
Z-Score = (Current Spread - Mean Spread) / Std Dev of Spread
Entry rules:
Z > +2.0: Enter trade (sell A, buy B) — spread too wide
Z < -2.0: Enter trade (buy A, sell B) — spread too narrow
Exit rules:
|Z| < 0.5: Close position, take profit
|Z| > 3.5: Consider stop-loss (spread may be breaking down)
Position sizing:
Long leg: +1 unit of Stock B
Short leg: -beta units of Stock A
(beta = hedge ratio, ensuring dollar-neutral position)
Why the Hedge Ratio Matters
A critical technical point: the long and short positions in a pairs trade must be sized correctly to create a truly market-neutral position. The hedge ratio (beta from the cointegrating regression) tells you how many units of Stock A to short for every unit of Stock B you buy (or vice versa).
If you simply buy £10,000 of Lloyds and sell £10,000 of Barclays, you have a dollar-neutral position but not a beta-neutral position — if Barclays is more volatile than Lloyds, your combined position has a directional bias. The correct approach is to scale the position sizes such that the market exposure (beta * position value) is equal on both legs.
Fintiq's Pairs tab calculates the hedge ratio automatically from the cointegrating regression and displays both the suggested position sizes and the resulting market neutrality of the trade.