A gilt fund expects the 2s10s curve to steepen. Size a DV01-neutral steepener that buys Rs 100 crore of 2-year bonds (duration 1.87) against 10-year bonds (duration 7.0), and work out the P&L if the 2-year falls 20 basis points and the 10-year rises 20.

Sell about Rs 26.7 crore of 10-year bonds; if the 2-year falls 20 and the 10-year rises 20, the trade makes about Rs 74.8 lakh. Each leg moves Rs 1.87 lakh per basis point, so the P&L is Rs 1.87 lakh times the 40 basis point change in slope. A parallel move of any size makes nothing. Holding it costs about Rs 6 lakh a year of carry, about 3.2 basis points of steepening.

A seesaw balances on weight times distance from the pivot, not on weight alone: a child far out balances an adult near the middle. A curve trade balances when each leg gains or loses the same rupees for a one basis point move, and long bonds move far more per rupee than short ones. Rs 100 crore of 2-year at duration 1.87 has a DV01The rupee change in a position value for a one basis point, 0.01%, change in its yield. of Rs 100 crore times 1.87 times 0.0001, Rs 1.87 lakh. Each rupee of 10-year is 7.0 over 1.87, about 3.7 times as sensitive, so only Rs 26.71 crore is needed for the same Rs 1.87 lakh.

The 2-year falls 20 basis points, so the long 2-year gains Rs 1.87 lakh times 20, Rs 37.4 lakh. The 10-year rises 20, so the bonds sold would have lost Rs 1.87 lakh times 20, which the fund avoids, a gain of Rs 37.4 lakh against holding them. Total Rs 74.8 lakh, which is simply Rs 1.87 lakh times the 40 basis point change in the spread. Any steepening of 40 basis points pays the same, whether it comes from the short end falling, the long end rising, or both; any parallel move pays nothing.

The trade gives up income. It earns 6.6% on Rs 100 crore of 2-year, but gives up 6.5% on Rs 73.3 crore of treasury bills and 7.1% on Rs 26.7 crore of 10-year. Net, it costs about Rs 6.0 lakh a year, so the curve must steepen about 3.2 basis points a year just to pay for holding the position, before any roll-down effects, which this simple count ignores. The trade also misses if the curve flattens: a 40 basis point flattening loses Rs 74.8 lakh. And DV01 neutrality holds only for small moves; after a large move the durations change and the legs need resizing.

Say what the trade expresses, too. A steepener of this kind usually reflects a view that the central bank will ease, pulling short yields down, or that long yields will rise on supply or inflation worries. If the view is really about easing, the manager should say so, because a bull steepener and a bear steepener come from different economies even though this trade pays the same in both.