From 1 Jul 2025 to 15 Sep 2026 Nifty and Bank Nifty rose and fell together almost every day. Their daily returns correlated at 0.91. Over the same 300 sessions the Nifty ended 9.5% below where it began and Bank Nifty 2.9% below. Two series that move together day to day still ended the stretch far apart. A pair trade is a bet that a gap like that closes, and whether it does depends on something correlation does not measure. This lesson explains the trade, the difference between correlation and cointegration, and how to test the difference on real closes. Every figure comes from NSE end of day files, dated and not live.
3By the end you can
- Explain a pair trade, its spread, the hedge ratio and the z score.
- Say the difference between correlation and cointegration and read a unit root test on a spread.
- Name the India specific limits on pairs, and why the pair must be judged on days it was not fitted on.
The idea, plainly
A pair trade holds one thing long and a related thing short, in proportion. If both rise or fall together, the two legs largely cancel. What is left is the spread, the gap between the two. The bet is that the gap goes back to where it usually sits.
A pair is judged on data it was not fitted on
Read 3 more paragraphs, 301 words
The spread needs a recipe. Take the log of each price. Regress one on the other over a formation window and the slope is the hedge ratio, the amount of the second leg held against the first. The spread is the first log price less the hedge ratio times the second, less the constant from the regression. To judge how far the spread has strayed, subtract its average and divide by its usual size. That is the z score. A z of two says the gap is two usual sizes from home. Many people act when it passes two. That is a habit, not a law.
Now the point of the lesson. Correlation asks whether the changes of two prices move together. Cointegration asks whether the gap between them stays near a home. Picture two walkers heading the same way. Their steps agree, so they are correlated, yet they can drift apart for as long as they walk. Tie them with a rope and the distance keeps coming back. Only the rope makes a pair trade, and it is a property of the spread, which correlation says nothing about.
The test for a rope is a unit root test on the spread. This one is the Engle Granger step: the regression first, then the Dickey Fuller statistic of the residual spread. The critical values are stricter than the ordinary tables, because the hedge ratio was chosen from the same data and makes the spread look tamer than it is. At the usual five percent level the statistic has to be below −3.34 in the Engle Granger tables. A second number, the half life, says how many sessions the gap takes to close half the distance. A half life that is long next to the sample is no use for a trade.
Worked example: Nifty and Bank Nifty, 1 Jul 2025 to 15 Sep 2026
I picked these two because their closes are in the files, not because they are a good pair. They share many of their biggest stocks, which is one reason they move together and one reason they are a poor pair in practice. Here are the 300 closes, rebased to a common start, with the rolling z score of the spread below.
The two indices move together, and still the gap wandered
Moving together day by day, the two still ended the stretch far apart
Fit on the first part, judge on the rest
- Formation window opens
First close in the file. The hedge ratio and the spread's average and size are fitted from here.
- Formation window ends
Everything fitted so far is frozen.
- Test window opens
The frozen ratio is carried forward on days it never saw.
- Test window ends
Last close in the file.
- Daily returns move together: yes.
- The spread stays near a home: no.
- A hedge ratio fitted early holds later: no.
Read 3 more paragraphs, 197 words
On daily returns the pair looks tied. On the log prices the correlation was 0.72, lower than on returns, and the spread tells the real story. The Dickey Fuller statistic of the full sample spread came to −0.49, nowhere near the cutoff. So the data give no reason to think the gap has a home. A rope would have shown a statistic far below it. The two walkers share a direction, and that is all they share.
Does it matter if I had looked only at the early part? I did the more honest test. I fitted the hedge ratio on the first half of the sessions, up to 4 Feb 2026, and carried it unchanged through the second half.
On the later days the spread did not return. Measured in the formation window's own standard deviations, it ended 7.5 below its formation average, and on no single session of the test window was it back at that average. A trader who had met a gap of two usual sizes in the test window would have faced more of the same, not a return. The pair had been fitted well and had not been tied.
Read the chart yourself
Use the pair chart above. In the upper panel note which index sits higher at the right edge. In the lower panel count how many sessions the z score line is beyond two on either side. Then check, for one of those days, whether the gap had closed a week later. Do it for a few days and write down how many closed and how many widened. Nothing here is a rule, and a handful of days proves nothing, but the habit of asking what came next is the habit a test makes formal.
The term this section turns on: Z score
Where this meets India
Most traders think of pairs as two stocks. I know of no NSE or SEBI list of pairs. The lists online are screens built by third parties on past prices, and pairs break. NSE publishes the stocks that have futures and options, and their lot sizes, and nothing about which stocks belong together. Several Indian features bend the trade, and each one is a cost or a limit that a paper spread does not show. In the cash market a retail short sale has to be closed the same day, and stock lending is thin, so both legs are usually stock futures. Lot sizes differ, so the hedge ratio comes in lumps. Take one lot of Nifty and one of Bank Nifty at the last closes: the first is 23,118.60 times 65 units and the second 55,794.75 times 30 units, and the two values are not equal, so a whole number of lots leaves part of the position unhedged. Monthly futures force a roll. A stock in the F&O ban period blocks new positions in that leg. And each futures leg pays STT of 0.05% on the sell side. The short answers are on the pages for pair trading and for cointegration against correlation. The longer treatment is module A23, and the testing toolkit is in module A22.
The common mistake
The belief: These two move together at 0.91, so any gap between them will close.
A correlation of daily returns is silent about the level of the gap. In this sample the daily return correlation was high and the gap ended far wider than it began. Over the 300 sessions Nifty changed by −9.5% and Bank Nifty by −2.9%, and the fitted spread did not come home on any test day. Look for evidence about the spread itself: a unit root test with the strict tables, a half life short against the sample, and a result that survives on days the fit never saw. Even then a pair can break.
Key takeaways
- A pair trade bets on the gap between two prices, not their direction.
- Correlation is about changes. Cointegration is about the gap staying near a home.
- Test the spread with strict tables, then judge it on later days.
- A long half life next to the sample means no trade.
- India: both legs are usually stock futures, with lumpy lots and monthly rolls.
- No NSE pair list exists. Online lists are screens on past prices.
Two terms to hold on to from 18.3
Before you trade. Derivatives trading carries a high risk of loss. SEBI's study "Profitability of Individual Traders in the Equity Derivatives Segment (FY25 to FY26)" (August 2026) found that 87.7% of individual traders in equity F&O made net losses in FY26, with aggregate net losses of Rs 91,685 crore. Read the SEBI study