Two bank stocks have 0.92 daily return correlation but their price ratio drifted from 1.0 to 1.6 over three years; a second pair has 0.55 correlation but a stationary spread with an ADF p-value of 0.01. Which pair do you trade?

Trade pair B. Correlation of 0.92 measures co-movement of daily returns and is blind to a slow drift: Mitravan's 17% a year of outperformance is 0.067% a day, invisible inside daily noise of 0.63%, and a hedge against it loses steadily. Pair B's spread is stationary at two standard deviations rich, about 8.3%; with a 10-day half-life the expected gain over 20 days is about Rs 62 lakh on Rs 10 crore a leg, against Rs 4 lakh of costs and daily noise near Rs 15 lakh.

Only that the daily moves point the same way. Two runners who match each other stride for stride look identical for any ten seconds you watch; if one is 1% faster, an hour later they are a lap apart. Correlation looks at the strides. With 25% volatility each and correlation 0.92, the daily return difference has volatility 10% a year, about 0.63% a day, and the 17% a year differential that took the ratio from 1.0 to 1.6 is only 0.067% a day, far too small for correlation to notice. Over three years that differential adds up to 0.47 in log terms, which is 2.7 standard deviations of the spread's random noise: a trend, not a wobble. The ADF p-value of 0.62 says the same thing formally: the ratio behaves like a random walk with drift, and there is no level it is pulled back to.

Put a trade on it and see what happens. Long Sahavasi, short Mitravan over the past three years was a quiet position with 10% volatility that lost about 17% a year: a Sharpe ratio near minus 1.7. The high correlation made it feel safe every single day while it bled. A candidate who picks pair A because 0.92 is a big number has confused a hedge that is quiet with a hedge that is anchored.

It tests the levels, not the returns. Two prices are cointegratedTwo non-stationary price series are cointegrated when some fixed combination of them, here the log price spread, is stationary and returns to a mean. when a fixed combination of them is stationary, so that the spread has a mean it keeps returning to. The ADF test asks whether the spread has a unit root, meaning it wanders without an anchor; a p-value of 0.01 rejects that at the 1% level. The fitted half-life of 10 days means the spread closes half of any gap in ten trading days, which with daily innovations of 1.49% gives a stationary standard deviation of about 4.2%, so two standard deviations is a spread of 8.3%. That is the number the trade is built on: a gap of 8.3% that is expected to halve in ten days.

Say the limits before the interviewer does. A p-value from three years of daily data can be fooled by one long mean-reverting episode, and a spread that was stationary in sample breaks the day one cement company announces an acquisition or a capacity doubling. The 0.55 correlation also has a cost: day-to-day noise on the spread is 1.49%, about Rs 15 lakh a day on Rs 10 crore a leg, more than twice pair A's. Pair B is the right trade and the rougher ride.

Short the rich stock and buy the cheap one, Rs 10 crore each way. The spread is 8.3% rich; with half-life 10 days its expected level after 20 days is 2.1%, so the expected gross gain is 6.2% of a leg, about Rs 62 lakh, against costs of 20 bps on each leg, Rs 4 lakh. Net about Rs 58 lakh expected, with daily swings near Rs 15 lakh, so a bad week can erase the expected gain several times over before the convergence arrives. Set the exit rules now: take profit near the mean, cut if the spread reaches three standard deviations or if a company-specific event changes the relationship, and re-estimate the half-life monthly, because a lengthening half-life is the first sign the anchor is slipping.

Close with the decision in one sentence: a pairs trade is a bet that a spread returns to its mean, so it is chosen on the test of the levels, and the correlation of returns only tells you how bumpy the wait will be.