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FRM Part I · FRM Exam Part I

Interest Rate Futures for FRM Part I

Interest rate futures are contracts whose payoff depends on a bond price or a short-term rate. Fix the day count and quote first, then size a duration hedge: N = (D_target − D_portfolio) × portfolio value ÷ (D_futures × futures price). Negative N means short futures. For a full hedge, D_target is zero, so a bond holder goes short; a future investor goes long.

What this chapter covers

This chapter covers how interest rate futures are quoted, priced and used. You start with day count and quoting conventions, because every later calculation depends on them. You then move to Treasury bond and note futures, where the cheapest-to-deliver bond and the conversion factor drive the price. Next come short-term rate futures such as SOFR futures (the successor to Eurodollar futures, which ended with LIBOR), where the quote is 100 minus a rate. Last is duration-based hedging, which turns the contracts into a risk-management tool.

The chapter builds on time value of money and bond pricing, and it uses duration and DV01 from bond valuation. It also links to forwards and futures pricing, since cost-of-carry logic carries over, with coupon income playing the role of a yield.

Questions are usually numerical and short. You may be asked to compute an accrued interest amount, a futures invoice price, a contract's implied rate, or a number of contracts to hedge a bond portfolio. Each is a few steps with a standard formula. Accuracy with conventions is what separates a right answer from a near miss.

This chapter is worth your effort because it is formula-driven and predictable. The questions reward a clear method rather than deep theory, so a candidate who practises each calculation type can pick up marks quickly. It also reinforces duration, DV01 and hedging, which appear in other parts of the paper, so time spent here pays off twice. GARP does not publish topic weights as marks, so treat it as a core area and not an optional one.

Interest Rate Futures: topics in the order to study them

  1. 1Day Count Conventions and Quoting ConventionsAccrued interest, prices and rates in every later topic depend on these conventions, so learn them first.
  2. 2Treasury Bond and Treasury Note FuturesThis applies the quoting rules to a real contract and introduces conversion factors and cheapest-to-deliver, which you need before hedging.
  3. 3Short-Term Rate Futures (SOFR, Formerly Eurodollar)The 100 minus rate quote and tick value are simpler once you are used to futures mechanics, and they bring in convexity and forward rate ideas. SOFR futures replaced Eurodollar futures after LIBOR ended.
  4. 4Duration-Based Hedging with Interest Rate FuturesThis ties everything together, using the contract prices and durations from earlier topics to size a hedge.

How to prepare Interest Rate Futures

Treat this chapter as a set of calculation types. Learn each formula, then drill it until the steps are automatic.

  1. Write down the day count rules for Treasuries (actual/actual), corporate and municipal bonds (30/360, with 180 days in a half-year coupon period) and money market instruments (actual/360), and practise one accrued interest calculation for each, counting days under that instrument's convention.
  2. Work through the T-bond futures price steps: the cash price of the deliverable, the conversion factor, and the quoted futures price. Use cash received = (futures quote × conversion factor) + accrued interest, and understand why the cheapest-to-deliver bond minimises the cost of delivery against the futures.
  3. Practise short-term rate futures such as SOFR futures (formerly Eurodollar): price = 100 − rate, so a quote of 97.50 implies a 2.50% rate. Compute the tick value from the contract's notional and the accrual period. A 3-month SOFR contract with $1,000,000 notional is worth $1,000,000 × 0.0001 × 3 ÷ 12 = $25 per basis point, so a fall in the quote from 97.50 to 97.40 (10 basis points) costs a long position 10 × $25 = $250. Then do some more gain and loss questions.
  4. Learn the duration hedge ratio and use it on several portfolios: N = (D_target − D_portfolio) × V_P ÷ (D_F × F), where V_P is the portfolio value, D_F is the futures duration and F is the futures price. A negative N means short futures; a positive N means long. For a full hedge, D_target = 0, so N = −(D_portfolio × V_P) ÷ (D_F × F). The direction depends on which way your risk runs: holders of bonds short futures, and future investors go long.
  5. Use a financial calculator for bond price, yield and accrued interest checks, and confirm each answer with a quick sense check on size and direction.
  6. Finish with timed mixed sets. Allow about two minutes a question, since the exam has 100 questions in 4 hours, and review every miss by naming the convention or formula you misapplied.

Common mistakes in Interest Rate Futures

  • Using the wrong day count for the instrument

    Fix: Before any calculation, name the instrument and write its convention beside the numbers.

  • Reading Treasury futures quotes as decimals

    Fix: Convert immediately: 110-16 = 110 + 16 ÷ 32 = 110.5.

  • Forgetting accrued interest or the conversion factor in delivery calculations

    Fix: Write the full cash formula each time and tick off each term.

  • Taking the wrong side of the hedge

    Fix: Ask whether you lose when rates rise or fall, then take the futures position that gains in that case.

  • Mixing up price and rate in short-term futures

    Fix: State that a rise in the quote means a fall in the rate, and check this against the sign of the gain.

  • Using inconsistent durations in the hedge ratio

    Fix: Confirm both durations are on the same basis, and use the cheapest-to-deliver bond's duration for the futures.

Last-day revision: Interest Rate Futures

  • Treasury notes and bonds use actual/actual; corporate and municipal bonds use 30/360 (180 days in a half-year coupon period); money market instruments use actual/360.
  • Accrued interest = coupon per period × days since last coupon ÷ days in the coupon period, with days counted under the convention: actual days for Treasuries, 30/360 days (180 in a half-year period) for corporates and municipals.
  • Treasury futures are quoted in points and 32nds of a point, so 110-16 means 110 and 16/32.
  • Cash received by the short = (quoted futures price × conversion factor) + accrued interest.
  • The short chooses the cheapest-to-deliver bond: compute quoted bond price − (futures quote × conversion factor) for each deliverable bond and pick the one with the smallest value.
  • Short-term rate futures such as SOFR futures (formerly Eurodollar) are quoted as 100 − rate, so a higher price means a lower rate.
  • When rates rise, a long position in rate futures loses and a short gains.
  • The full-hedge ratio is N = −(D_P × V_P) ÷ (D_F × F), where the sign is set by the direction of risk and a negative N means short. To move to a target duration, use (D_target − D_P) in place of D_P, with the sign the same way.
  • To hedge a bond portfolio against rising rates, you short futures; a party who will invest later and fears falling rates goes long.
  • Duration hedging protects only against small parallel shifts in the yield curve, and basis risk remains.
  • DV01 matching gives N = DV01 of portfolio ÷ DV01 of one futures contract.
  • Sense check every answer: direction of the trade, sign of the P&L and size of the number.

Interest Rate Futures practice questions

Interest Rate Futures in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Interest Rate Futures: frequently asked questions

How should I read a Treasury bond futures quote?

The quote is in points and 32nds of a point. So 98-08 means 98 plus 8/32, which is 98.25. Convert it to a decimal before you multiply by the conversion factor or contract size.

What is the cheapest-to-deliver bond?

It is the deliverable bond that costs the short the least to buy relative to what the short receives on delivery. For each bond, compute quoted bond price − (futures quote × conversion factor). The bond with the smallest value is cheapest. Accrued interest is paid on purchase and received on delivery, so it does not change this comparison of quoted prices.

How do I calculate the number of futures contracts for a hedge?

For a full duration hedge, divide the portfolio's value times its duration by the futures price times the futures duration. If you want to change duration to a target, use the difference between target and current duration in the numerator. Then choose short or long based on the direction of the risk.

Do I need to memorise many formulas for this chapter?

Not many. You need the accrued interest formula, the delivery cash formula, the 100 minus rate quote and the hedge ratio. The harder part is applying the conventions correctly, so practise them with numbers rather than only reading them.