A treasury holds Rs 800 crore of 10-year government bonds with modified duration 7.1 against a DV01 limit of Rs 25 lakh. Measure the breach and size an interest rate swap that brings the book inside the limit.

The book's DV01 is Rs 56.8 lakh, Rs 31.8 lakh over the limit, and at least Rs 707 crore of pay-fixed swap is needed to cure it. Each Rs 100 crore of swap offsets Rs 4.5 lakh. Rounding up to Rs 750 crore leaves a net DV01 of Rs 23.05 lakh, a small buffer under the limit. The book then carries swap spread risk instead: bond yields and swap rates do not move one for one.

Modified duration says how many per cent the price moves for a one point move in yield. A seesaw is a fair picture: the longer the plank on the bond's side, the further it swings for the same push. DV01The change in a position value, in rupees, for a one basis point, 0.01 percentage point, change in yield. turns that percentage into rupees for one basis point: Rs 800 crore times 7.1 times 0.0001, which is Rs 56.8 lakh. A 25 basis point rise, not a rare week, costs the desk about Rs 14.2 crore.

Size the hedge in the same unit as the limit. The book must shed Rs 31.8 lakh of DV01, and each Rs 100 crore of pay-fixed swap sheds Rs 4.5 lakh. Rs 31.8 lakh divided by Rs 4.5 lakh is 7.07 lots of Rs 100 crore, so at least Rs 707 crore of notional. Landing exactly on the limit leaves no room for the next trade or for duration drifting as yields move, so round to Rs 750 crore: the swap offsets Rs 33.75 lakh and the net book sits at Rs 23.05 lakh.

The hedged book is long government bonds and short swaps, so it no longer cares much where rates go, but it does care about the gap between them. If swap rates rise 10 basis points less than bond yields, the Rs 750 crore swap under-hedges by about Rs 3.4 crore, because Rs 33.75 lakh times 10 is about Rs 3.4 crore. That swap spreadThe gap between the swap rate and the government bond yield of the same maturity; it moves with bank credit, supply and demand. risk is smaller than the outright rate risk, but it is not zero, and the desk's limits should measure it separately.

A full hedge would take about Rs 1,262 crore of notional, which few desks want: the point of holding the bonds is usually to earn their carry. The desk has done its job when it brings DV01 under the limit with a buffer, reports the breach and the date it occurred, and adds swap spread to the risks it watches. Once the pledge lifts, selling part of the bonds is the cleaner cure.