Build a DV01-neutral two-year versus ten-year swap steepener with Rs 100 crore of ten-year, given DV01s of Rs 190 and Rs 700 per crore. Size the two-year leg and find the P&L if two-year rates fall 20 bp and ten-year rates rise 5 bp.

Receive fixed on about Rs 368.4 crore of two-year swaps and pay fixed on Rs 100 crore of ten-year: each leg then carries Rs 70,000 per basis point. The two-year leg makes 20 times Rs 70,000, Rs 14.0 lakh, and the ten-year leg 5 times Rs 70,000, Rs 3.5 lakh, so the trade makes Rs 17.5 lakh on 25 bp of steepening. A parallel move makes nothing, because the legs offset. What is left is a bet on the spread, with curve beta, carry and drift in the DV01s as the risks.

Picture a plank resting on two bricks, one short and one tall. If you are paid on how steep the plank is, you do not care whether someone raises the whole floor; you care whether the short brick sinks or the tall one grows. A steepener is paid when the long rate rises relative to the short rate, so the desk receives fixed on the two-year, which gains when two-year rates fall, and pays fixed on the ten-year, which gains when ten-year rates rise. Each leg's sensitivity is measured by its DV01The change in the value of a position for a one basis point move in rates, in rupees. For a swap it grows roughly with the tenor and the notional., and the trick of the trade is to make the two DV01s equal so that a parallel move in both rates cancels out.

The ten-year leg carries 100 times Rs 700, Rs 70,000 for every basis point. To carry the same Rs 70,000 on the two-year leg at Rs 190 a crore the desk needs Rs 368.42 crore of notional, which rounds in practice to Rs 368 crore or Rs 370 crore depending on the ticket size. The gross notional is about Rs 468 crore, which is what the desk's counterparty lines and margin will see, even though the net rate risk to a parallel move is close to zero.

Each leg's P&L is its DV01 times the move, with the sign set by the side. The two-year rate falls 20 bp and the desk receives fixed, so that leg gains 20 times Rs 70,000, Rs 14.0 lakh; the ten-year rate rises 5 bp and the desk pays fixed, so that leg gains 5 times Rs 70,000, Rs 3.5 lakh; together Rs 17.5 lakh. The cleaner way to say it: the trade earns Rs 70,000 for every basis point the two-to-ten spread widens, and the spread went from 50 bp to 75 bp. The table checks the claim against moves the desk does not want to bet on.

Three things, each with a reason. DV01-neutral is not move-neutral: when rates reprice on a policy surprise, two-year rates usually move more than ten-year rates, so a sharp rise in all rates often flattens the curve and costs this trade money even though each basis point is balanced. Desks that worry about this weight the legs by the historical ratio of moves, a beta weighting, rather than one for one. Second, carry and roll-down are not zero: the desk receives one fixed rate and pays another on very different notionals, against floating legs that also differ, and the net running cost or income should be computed before the trade, because a view that takes six months to arrive can be eaten by negative carry. Third, the DV01s drift: in three months the two-year swap is a 1.75-year swap with a smaller DV01, so the hedge ratio has to be reset.

Say the limits of the working. The DV01s are given per crore and treated as constant, which is fine for moves of a few tens of basis points but ignores convexity; the curve in the figure is illustrative; and the P&L is the immediate mark, before any carry. The judgement for the desk is that the trade expresses the view it holds, the spread, and not the one it does not hold, the level, which is the point of sizing it this way.