Bond futures and hedging

A bond future is an agreement, made today, to buy or sell a government bond on a later date at a price fixed today. It trades on an exchange, so it is quick and cheap to deal in large size. The ICE Long Gilt future, for example, covers £100,000 of gilts per contract.

Bond futures run on a quarterly cycle, and each month has a letter: H for March, M for June, U for September and Z for December. Few traders wait for delivery. Most close their position, or roll it into the next contract, in the days before the delivery month.

A bond future doesn’t name one bond: the seller can deliver any gilt with 8¾ to 13 years left. A 6% gilt is worth more than a 2% one, so each gets a conversion factor, roughly its price at a 4% yield divided by 100. Coupons above 4% give factors above 1; coupons below 4%, factors below 1.

When a bond is delivered, the seller receives the invoice price: the futures price × the bond’s conversion factor, plus accrued interest. With the future at 95, a factor of 0.9 and accrued interest of 1.0, that is 95 × 0.9 + 1.0 = 86.5 per 100.

The seller chooses which bond to deliver, so it picks the one that costs least to buy compared with what it will be paid: the cheapest-to-deliver. With the future at 100, bond A costs 80.5 against 100 × 0.80 = 80.0, and bond B costs 90.2 against 90.0. B costs only 0.2 more than it earns, so B is delivered, and the future moves like B.

Because the future tracks its cheapest-to-deliver bond, its DV01 comes from that bond: futures DV01 ≈ the bond’s DV01 ÷ its conversion factor. If the cheapest gilt moves £82 per bp for £100,000 and its factor is 0.93, one future moves about £82 ÷ 0.93 = £88 per bp.

To hedge, match DV01s: contracts = your position’s DV01 ÷ the futures DV01. A gilt holding that loses £33,000 per bp needs about £33,000 ÷ £88 = 375 futures sold. Then a rise in yields costs the bonds what the short futures make.

Futures can also change a portfolio’s duration without touching the bonds. The DV01 to add = (new duration − old duration) × portfolio value × 0.0001: buy futures to add it, sell to remove it. Cutting £100m from duration 6 to 5 removes £10,000 per bp; with a futures DV01 of £80, sell 125 contracts.

A DV01 hedge only cancels moves where all yields shift together. Hedge 30-year gilts with Long Gilt futures, which follow a 10-year gilt, and you still lose if 30-year yields rise more than 10-year ones. That leftover is curve risk. The gap between your bonds and the cheapest-to-deliver is basis risk.