Pair trading calculator
Spread z-score and hedge ratio.
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Cointegration test
Do two markets stay tied together, or only look alike? The Engle-Granger test on your two price lists, before you trade the spread.
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The two markets
The test
Not cointegrated: the test statistic -1.48 is above -3.41, the 5% line for 80 days. The spread between the two has wandered like a random walk, so a pair trade on it has nothing that pulls it back.
- Hedge ratio
- 1.100: the spread is the second's log price minus 1.100 times the first's, so a 1% move in the first has gone with about 1.10% in the second.
- Critical values
- -4.04 at 1%, -3.41 at 5% and -3.10 at 10% for 80 days. They are stricter than a plain Dickey-Fuller test because the hedge ratio was fitted to the same prices.
- Correlation is not enough
- The prices are 0.55 correlated, yet not cointegrated: trending the same way does not tie them together over time.
- Spread now
- +2.00 standard deviations from its average. About 9.3 days for a gap in the spread to halve, though that pull did not pass the test.
- Read it with care
- A pair can be cointegrated for years and then break apart. Check the test on several stretches, as in the table, and keep a stop on the spread.
The same test on the most recent days only: the hedge ratio, the statistic and whether it passes at 10% or better.
| Days | Hedge ratio | Statistic | Cointegrated |
|---|---|---|---|
| Last 40 | 0.755 | -1.10 | No |
| Last 60 | 0.426 | -0.59 | No |
| All 80 | 1.100 | -1.48 | No |
Education only, not investment advice. The answer comes from the numbers you typed in, not from your account or the market. Simulated results are hypothetical and have limits: real trading has slippage, gaps, changing results and emotions. Trading leveraged products can lose money quickly, including all of it. Risk warning
Educational only, not financial advice; trading involves risk.
Correlated is not the same as tied together
Two markets can rise and fall on the same days and still drift apart for years. A pair trade, long one and short the other, only works when something pulls the gap back. Robert Engle and Clive Granger's test, which shared a Nobel prize in 2003, checks exactly that: it fits the hedge ratio, then asks whether the spread behaves like a random walk or keeps returning to its average.
Size the two legs with the pair trading calculator, see how fast the spread closes with the mean reversion half-life calculator, compare day-to-day moves with the correlation calculator, and size the trade with the position size calculator.
Not advice. A test on the prices you type; a pair that held together can break apart.
Next tools
Mean reversion half-life calculator
How fast do gaps close?
Correlation calculator
How closely two markets move together.
Pricing
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Baroq never holds your money and never trades for you. Educational only, not financial advice; trading involves risk.