Interest-Rate Futures

A pension fund's bond portfolio has a duration of seven years — a nasty number if the Fed surprises the market next week. Selling $50 million of actual bonds to cut that exposure is slow, moves the market, and undoes a carefully built portfolio. What the desk reaches for instead is a listed, hugely liquid interest-rate future — a contract that can trim (or add) exactly the amount of rate exposure needed, in seconds, without touching a single underlying bond. This closing lesson of the module looks at the two workhorse contracts and how duration turns them into a precise hedge.

Two families of contract

Treasury bond futures obligate the short to deliver an eligible government bond at contract expiry, against a standardized $100,000 face-value contract. "Eligible" covers a whole basket of outstanding bonds within a maturity range, not one specific bond — the short gets to choose which one to deliver, using a conversion factor published for each eligible bond that rescales it to an equivalent 6%-coupon notional bond. Because the conversion factors are only an approximation, one bond in the basket is always slightly cheaper for the short to deliver than the others — the cheapest-to-deliver (CTD) bond — and the futures price tracks that bond's price (divided by its conversion factor) far more closely than any other bond in the basket. For hedging purposes, a Treasury future essentially behaves like a position in its current CTD bond.

SOFR futures (successor to the old Eurodollar futures) are simpler: cash-settled contracts on a $1 million notional, referencing the average SOFR rate over a 3-month period, with no delivery and no CTD complication at all. Following a heritage convention, they are quoted as

\text{Futures price} = 100 - R

where R is the (percentage) interest rate — so a quote of 95.25 implies a 4.75% rate. A strip of these futures, at consecutive maturities, is exactly the raw material used to build the term SOFR curve mentioned back in the first lesson of this module — and the same instruments reappear as the building block for rate caps and floors much later in the course.

	Treasury bond futures	SOFR futures
Settlement	Physical delivery of a bond	Cash-settled
Underlying	A basket of eligible T-bonds	3-month average SOFR
Contract size	$100,000 face value	$1,000,000 notional
Quoting quirk	Price in 32nds of a point	Price = $100 - R$
Main use here	Hedging bond-portfolio duration	Building the short end of the rate curve

Duration-based hedging with bond futures

Treat the futures contract as a proxy position in its CTD bond, with duration D_F and dollar value per contract V_F (the quoted futures price, as a fraction of par, times the $100,000 contract size). To offset the dollar duration of a portfolio worth P with duration D_P, choose the number of contracts

N^{*} = -\,\frac{P\,D_P}{V_F\,D_F}.

The minus sign is the whole point: a long bond portfolio (positive duration, loses value when rates rise) is hedged by going short futures, so a loss on the portfolio is offset by a gain on the short futures position when rates rise (and vice versa).

Worked example. The pension fund's $50 million portfolio has duration D_P = 7 years. The T-bond future is quoted at 118\text{-}16 (bond-futures convention: 118 and 16/32 = 0.5, i.e. 118.5% of par), so V_F = 1.185 \times \$100{,}000 = \$118{,}500. Its CTD bond has duration D_F = 8.5 years. Then

N^{*} = -\frac{50{,}000{,}000 \times 7}{118{,}500 \times 8.5} = -\frac{350{,}000{,}000}{1{,}007{,}250} \approx -347.5.

Round to the nearest whole contract: short about 348 contracts. If yields jump, the loss on the $50 million bond book is (to first order) offset almost exactly by the gain on this short futures position — the fund has bought itself insurance without selling a single bond. This is the same duration-matching logic that reappears, generalized, as the minimum-variance hedge ratio later in the course, and the futures themselves become the building blocks for pricing models of the short rate further along still.

It looks backwards at first — why not just quote the rate directly? Because a rates desk already thinks in bond-price terms, where "price up" means "good for the holder" and "price down" means "bad." A rate quoted directly would flip that intuition: a trader who is bullish on falling rates would need to remember to sell a rate quote to profit from it. Quoting the contract as 100 - R instead makes a SOFR future behave exactly like a bond: its price rises when rates fall and falls when rates rise, so "go long if you expect rates to drop" is true here exactly as it is for an ordinary bond. The convention dates back to the original Eurodollar futures contract of 1981 and has simply stuck, carried over intact into SOFR's own futures when LIBOR was retired.

Two ways to get a duration-based futures hedge backwards:

Flipping the sign. A portfolio that is long bonds needs a short futures position to hedge against rising rates — going long futures on top of a long bond book doubles the rate exposure instead of cancelling it. Always re-derive the sign from first principles (does the hedge gain when the portfolio loses?) rather than memorizing "long hedges long."
Ignoring the conversion factor. The dollar value per futures contract is the quoted futures price times the $100,000 contract size — not the CTD bond's own market price, and not the futures price left unconverted from its 32nds quoting convention. Skipping either conversion silently scales the whole hedge ratio wrong, in a way that won't show up until the hedge fails to offset a real rate move.