Interest Rate Futures: Bond Futures, SOFR Futures, and Duration Hedging

A bond portfolio manager who fears rising rates has a problem: duration — the sensitivity of bond price to yield — is a continuous exposure baked into every holding. Selling bonds to reduce duration is expensive in transaction costs and disrupts the investment mandate. Interest rate futures offer a cheaper and reversible alternative. By shorting Treasury bond futures, the manager can reduce the portfolio's effective duration without touching a single bond.

This note develops the mechanics of the two most important interest rate futures contracts — Treasury bond futures and short-rate futures (Eurodollar/SOFR) — and the duration-based hedging formula that quantifies how many contracts to trade. Understanding these contracts requires two pieces of infrastructure first: day count conventions (which determine how bond accrued interest is calculated) and the cheapest-to-deliver (CTD) mechanism (which determines which bond actually changes hands at delivery).

• explain the three common day count conventions and compute accrued interest;
• describe how Treasury bond futures work: quotes, conversion factors, CTD selection;
• compute the theoretical futures price for a known CTD bond;
• explain how Eurodollar (or SOFR) futures lock in a short-term rate, and convert a quote to an interest rate;
• apply the convexity adjustment to convert a futures rate to a forward rate;
• use the duration-based hedge ratio to determine the number of contracts needed to hedge a bond portfolio.

1. Day count conventions
2. Treasury bond futures
3. Short-rate futures: Eurodollar and SOFR
4. Duration-based hedging
5. Adjusting portfolio duration