A long-short pair uses stock A (beta 1.2, size exposure 0.5) and stock B (beta 0.8, size exposure -0.3) on Rs 10 crore of gross exposure. Find market-neutral weights, then show what it costs to neutralise size as well with an index future.

Market neutral is Rs 4 crore long A and Rs 6 crore short B, which leaves +3.8 of size exposure that two stocks cannot remove. One small-cap future removes it only by moving the weights to 6.35 and 3.65, which raises annual risk from Rs 1.76 to 1.95 crore. Two futures keep the weights and trim risk to 1.73. Size is about 3% of the variance, so run the 4 / 6 pair and hedge size at book level.

A seesaw balances when weight times distance matches on both sides, not when the weights are equal. Beta neutrality needs long A times 1.2 to equal short B times 0.8, so the long leg is the smaller one: 1.2a = 0.8b with a + b = 10 gives a = Rs 4 crore long A and b = Rs 6 crore short B. A dollar-neutral 5 / 5 pair would carry 5 x 1.2 - 5 x 0.8 = +2.0 crore of market exposure, so a 10% market fall would cost about Rs 20 lakh for reasons unrelated to the view on A and B.

Count the knobs. With gross fixed, two stocks leave one free number, the split between them, and one free number can satisfy one condition. Here it cannot even try: long A adds +0.5 of size per rupee and short B adds +0.3, so the market-neutral pair carries 4 x 0.5 + 6 x 0.3 = +3.8 crore of size exposure, and every long A, short B pair is net small-cap. Removing it needs a third instrument whose size exposure can be traded against the stocks.

With the small-cap future, solve three conditions at once: gross of Rs 10 crore in stocks, zero market and zero size. The answer is Rs 6.35 crore long A, Rs 3.65 crore short B and Rs 4.27 crore short the small-cap future. The future cancels size but also brings beta of -1.1 per rupee, so the stocks must be re-weighted toward A to put that beta back. With both futures you leave the stocks at 4 / 6, short Rs 3.11 crore of the small-cap future to remove size and buy Rs 3.43 crore of the large-cap future to put back the market exposure the short added. Either way futures add gross, margin and roll cost; the second route adds Rs 6.54 crore of futures notional.

Split the risk. In the market-neutral pair, stock-specific risk is about Rs 1.73 crore a year and size risk is 3.8 x 8% = Rs 0.30 crore. Because the two add in squares, size is only about 3% of the variance, and removing it with one future backfires: moving weight into the more volatile stock A adds more stock-specific risk than the hedge takes out. Two futures do remove it cleanly, cutting risk only from 1.76 to 1.73. The view for Ilavari: run the market-neutral 4 / 6 pair and net size exposure across the whole book, where many pairs' tilts can offset before any future is bought.

The limitation is the risk model. Betas and size exposures are estimates with error, so a pair that is exactly neutral on paper carries some residual exposure in practice, and the exposures drift as prices move. Rebalance the hedge when the exposures move, not on a calendar.