A pension scheme has liabilities of Rs 1,200 crore with a duration of 14 and assets of Rs 1,000 crore with a duration of 5. What happens to the deficit if rates fall 100 basis points, and how much DV01 must be added to hedge half the liability rate risk?

A 100 basis point fall widens the deficit from Rs 200 crore to about Rs 318 crore, because liabilities gain Rs 168 crore and assets only Rs 50 crore. In DV01 terms liabilities move Rs 1.68 crore per basis point and assets Rs 0.50 crore, a 30% hedge. Hedging half the liability risk means asset DV01 of Rs 0.84 crore, so add Rs 0.34 crore per basis point, about Rs 283 crore of long gilts or a receive-fixed swap of about Rs 486 crore notional.

Think of saving for a child's college fees fixed in rupees ten years out. If the interest you can earn falls, you need more money today to reach the same sum, even though your existing deposits are worth a little more. A pension promise behaves like a very long bond the scheme has sold, so when rates fall its value rises by duration times the move: 14% of Rs 1,200 crore, Rs 168 crore. The assets also rise, but only 5% of Rs 1,000 crore, Rs 50 crore. The deficit widens to Rs 318 crore and the funding ratio falls from 83.3% to 76.8%.

Use DV01, the rupee change for one basis point, on each side. Liabilities move Rs 1.68 crore per basis point and assets Rs 0.50 crore, so the deficit widens by Rs 1.18 crore for every basis point rates fall. The ratio of the two, 30%, is the hedge ratio: the share of the liability rate risk the assets already offset. Notice that the rupee gap matters, not the duration gap alone, because the assets are smaller than the liabilities; even assets with a duration of 14 would only hedge 83% of the risk.

Half the liability rate risk is Rs 0.84 crore per basis point. The assets already provide Rs 0.50 crore, so the hedge needs only another Rs 0.34 crore per basis point, not Rs 0.84 crore. Counting the existing bonds is where many candidates over-hedge. Two ways to add it: switch about Rs 283 crore from equity into long government bonds with a modified duration near 12, or keep the equity and enter a receive-fixed interest rate swap of about Rs 486 crore notional at a duration near 7. The switch reduces expected return because it sells growth assets; the swap keeps the equity but brings collateral calls and counterparty limits, and whether a scheme like this may use derivatives at all depends on its trust deed and the current rules for such schemes, which must be confirmed.

A hedge works in both directions. If rates rise 100 basis points, the unhedged deficit would narrow to Rs 82 crore, but the hedged one only to Rs 116 crore. So the trustees are not buying protection for free; they are choosing to stop betting on rates. That is usually right for a scheme whose sponsor cannot easily fund a sudden deficit, and it is why hedge ratios are raised in steps, often when funding improves. Say the limits: duration is a straight-line approximation that understates a 100 basis point move on a duration-14 liability, the discount rate the actuary uses may not be the gilt yield the hedge tracks, and inflation-linked pensions need a separate hedge.