Two private banks, Sarvodh and Nimbal, usually trade 1.2x apart on price to book, with a standard deviation of 0.2x. Today the gap is 1.6x and the spread's half-life is about 60 days. Analyse the trade: entry, sizing, stop and what you expect to make.

The gap is two standard deviations wide, so short Sarvodh and buy Nimbal, expecting it to narrow to about 1.4x in 60 days. On Rs 10 crore a side that earns roughly Rs 0.67 to 1.43 crore, depending on which bank moves. Put the stop at 1.8x, three standard deviations, and size so the worst loss at the stop is Rs 5 crore: about Rs 35 crore a side. Before entering, check that nothing real has changed at either bank.

Two petrol pumps on the same road usually charge within a rupee of each other; when one suddenly charges five rupees more, customers drift across until the gap closes, unless one pump has started selling something different. A pairs trade bets that a price relationship between two similar businesses returns to its usual level, so you short the one that looks rich and buy the one that looks cheap. The gap is 1.6x against a mean of 1.2x and a standard deviation of 0.2x, a z-scoreHow many standard deviations a number sits from its average. A z-score of 2 means two standard deviations above. of +2. So you short Sarvodh and buy Nimbal. The market direction mostly cancels; what you own is the gap.

The expected gap after t days is 1.2 + 0.4 x 0.5 raised to t / 60: 1.48x after 30 days, 1.4x after 60, 1.3x after 120. What the 0.2x narrowing is worth in rupees depends on which bank moves, because a 0.1x change is 3.3% of Sarvodh's multiple but 7.1% of Nimbal's. With Rs 10 crore on each side, a 0.2x narrowing made entirely by Sarvodh falling earns Rs 0.67 crore; made entirely by Nimbal rising, Rs 1.43 crore; split evenly, Rs 1.05 crore.

Put the price stop at 1.8x, three standard deviations: a gap that wide happens rarely if the relationship still holds, so reaching it is evidence that it may not. Add a time stop at about 120 days, two half-lives; if the gap has not narrowed by then, the reversion speed you measured is wrong. Size from the worst loss at the stop: if Nimbal does all the widening, a 0.2x move loses Rs 1.43 crore per Rs 10 crore a side, so the Rs 5 crore budget allows about Rs 35 crore a side. Keeping equal rupees on each side leaves little market exposure, though bank betas differ and are worth checking.

A real change at one bank. Price to book gaps between banks track the gap in their return on equity, so if Nimbal's bad loans have jumped, or Sarvodh has just raised capital that will dilute its returns, the new gap may be the right one. Before trading a statistical gap, look for the fundamental reason it opened; if you find one, the pair is not cheap, it is changed. Also say the statistical limit: two years of data give only a handful of independent half-lives, so the 0.2x standard deviation and the 60-day half-life are themselves uncertain.