Analyse a pairs trade in Varnika Paints and Chitrangi Coatings: hedge ratio 1.2, spread z-score 2.3, half-life 12 days, spread standard deviation Rs 8. What are the expected profit, the holding time and a stop level, and what would break the relationship?

Short the spread at z = 2.3 and exit at 0.5: on the average path that takes about 26 days and earns Rs 14.4 a unit, Rs 1.44 lakh on 10,000 units before costs. A stop at z = 4.0 risks Rs 13.6 a unit; if the spread truly mean-reverts, it is hit only about 0.9% of the time, so a hit means the relationship has probably broken. Expected profit after costs is about Rs 1.13 lakh.

Two neighbouring tea stalls charge almost the same for a cup; if one suddenly charges Rs 5 more, customers drift to the other until the gap closes. A pairs trade bets that two similar companies' prices stay tied, so when the spread between them stretches, you sell the dear one and buy the cheap one and wait for the gap to close. Here Varnika is dear: the spread of Rs 34.0 is 2.3 standard deviations above its mean of Rs 15.6. Short 10,000 Varnika and buy 12,000 Chitrangi; the 1.2 hedge ratio makes the position roughly neutral to the paint sector moving as a whole.

A half-life of 12 days means the expected gap to the mean halves every 12 days: 2.3, then 1.15, then 0.58. To reach an exit at 0.5 takes ln(2.3 / 0.5) / ln 2 half-lives, about 26.4 days on the average path, and captures 1.8 standard deviations, Rs 14.4 a spread unit. On 10,000 units that is Rs 1.44 lakh. Costs at 5 basis points a leg each way on Rs 2,866 of gross exposure a unit come to Rs 2.87 a unit. Individual trades will scatter around 26 days; mean reversion sets the average pace, not the date.

Put the stop where the model says the move would be very unlikely, at z = 4.0, a loss of Rs 13.6 a unit. If the spread really reverts with this half-life, the chance of touching 4.0 before 0.5 is only about 0.9%, so reaching the stop is evidence that the relationship itself has changed, and the right response is to get out, not to add. With that probability, the expected profit is about Rs 11.3 a unit after costs, Rs 1.13 lakh in total. Add a time stop too: if the spread is still above 1.0 after three half-lives, 36 days, when the average path would be at 0.29, the half-life estimate is probably wrong.

The statistics describe the past; the economics decide the future. A pair breaks when something hits one company and not the other: an acquisition offer, a new plant or a lost distributor, a raw material that one uses far more than the other, or a shift in mix, such as one moving into industrial coatings while the other stays in home paint. Watch the hedge ratio and half-life on a rolling window; a half-life stretching from 12 days towards 40 is an early warning. Check the news on both names before entry: a 2.3 standard deviation gap that opened on an announcement is information, not noise. The limitation to say plainly: the 0.9% stop probability comes from the model, and the model is exactly what fails when the stop is hit.