Interest rate futures: the 100 minus rate convention
Short-term interest rate futures are quoted as 100 minus the rate, so the price rises when the rate falls. A long position gains when rates fall (like a lender); a short gains when rates rise (like a borrower). Each basis point is worth notional × 0.01% × the period length.
Before this: Forward rate agreements (FRAs): settlement and uses
On the exam
- Compare the value and price of forward and futures contracts
Compare interest rate futures with forward rate agreements (FRAs). Expect: the implied rate from a price, the basis point value, a gain or loss from a price move, and which position hedges a future borrowing or deposit.
How deeply to learn each part
- Know the idea
- Understand it in general. It frames other topics, but you will not calculate with it.
- Use it
- Understand it well enough to solve a question with it. Recognize when it applies.
- Memorize
- Learn it by heart. The exam will not give it to you.
You know this one. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still do.
You tested strong here. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still know it.
How are short-term interest rate futures quoted?
interest rate futures are contracts on a market reference rate (MRR) for a future period, such as a three-month rate starting in three months. They are the standardized, exchange-traded alternative to an FRA. Instead of quoting the rate, they quote a price.
This is the futures price 100 minus rate convention. A quote of 96.40 implies a rate of 100 − 96.40 = 3.60%. When rates are negative, the price is above 100. The price is not the price of a bond: it is simply a way to quote a rate so that the price rises when the rate falls.
A short-term interest rate futures contract is quoted at 96.4. The implied market reference rate (as a percentage) is closest to:
100 − 96.4 = 3.60%
Implied market reference rate3.60%
- 100−96.4=3.6
- 100ENTER96.4−3.6
ENTER enter (on the HP, puts the number on the stack)
Who gains when rates move?
The two sides are those of a lender and a borrower. The buyer of the future earns the reference rate and gains when it falls: long futures gains when rates fall . The seller pays the rate and gains when it rises. An FRA gives the same exposures from the other direction, which is the FRA equivalence : a long FRA (pay fixed, receive floating) behaves like a short future.
- Gains when rates RISE Memorize price falls (100 − rate)
- Short rate futures hedges a future borrowing
- Long FRA pays fixed, receives floating
-
- Gains when rates FALL Memorize price rises (100 − rate)
- Long rate futures hedges a future deposit or lending
- Short FRA receives fixed, pays floating
-
| Gains when rates rise | Gains when rates fall |
|---|---|
| Short rate futures; long FRA (pay fixed) | Long rate futures; short FRA (receive fixed) |
Exam tip Think of the price: it falls when rates rise. Whoever is short a falling price gains.
How much is a basis point worth?
The futures contract basis point value (BPV) is the cash gained or lost per basis point (0.01%) of rate movement. It depends on the notional and on the period of the underlying rate, because a month of interest is worth less than a quarter of interest.
The relationship is linear: each basis point is worth the same amount whether the rate rises or falls.
An interest rate futures contract has a notional of 1,000,000.00 on a rate covering 0.25 years. The value of one basis point per contract is closest to:
1,000,000.00 × 0.0001 × 0.25 = 25.00
BPV per contract25.00
- 1000000×0.0001×0.25=25
- 1000000ENTER0.0001×0.25×25
ENTER enter (on the HP, puts the number on the stack)
Try this 0 of 3
- As the short, push the rate up to 3.95%
- Switch the period to 6 months and watch the BPV
- Drag the rate below zero
At the entry price: no gain or loss. Move the rate to see who wins.
Show working
Quote: price = 100 − rate = 100 − 3.60 = 96.40. Entry 96.40 implies a rate of 3.60%.
BPV per contract = notional × 0.0001 × period = 1,000,000 × 0.0001 × 3/12 = USD 25.00.
Move: price 96.40 → 96.40 = 0.00 bp of price, so 0.00 bp in the short's favor.
P&L = 0 × 25 × 20 = USD 0.00.
FRA equivalent: a short futures position gains when rates rise, like a long FRA (pay fixed).
- 1000000×0.0001×0.25=25, the BPV per contract
- ×0×20=0.00, the total P&L
- 1000000ENTER0.0001×0.25×25, the BPV per contract
- 0×20×0.00, the total P&L
ENTER enter (on the HP, puts the number on the stack)
Move the rate and watch the price dial move the other way. Switch the position between long and short and see the profit or loss change sign, never size.
Take as the change in the price times 100 for a long position (a price rise is a gain), and reverse the sign for a short.
An investor is long 9 rate futures contracts, each on a notional of 1,000,000.00 for a 0.25-year rate. The price moves from 98.2 to 98.6. The gain (positive) or loss (negative) is closest to:
40 bp × 25.00 × 9 = 9,000.00
Gain (+) or loss (−), long9,000.00
- 98.6−98.2=×100=40 bp
- ×1000000×0.0001×0.25×9=9000
- 98.6ENTER98.2−100×40 bp
- 1000000×0.0001×0.25×9×9000
ENTER enter (on the HP, puts the number on the stack)
Go deeper Why 100 minus rate is not a bond price
A bond price at a given yield would be for a zero-coupon bond, which does not move one-for-one with the rate. The futures quote moves exactly 0.01 per basis point, which is why the BPV is constant. This linearity is what creates the convexity bias against FRAs in the next lesson.
Go deeper Strips of quarterly contracts
Rate futures exist for successive monthly or quarterly periods out to several years. A series of consecutive contracts (a strip) can hedge a longer floating-rate exposure period by period, which leads naturally to interest rate swaps.
Memorize this
MemorizeRate futures at a glance
| Rule | |
|---|---|
| Quote | (above 100 = negative rate) |
| Long futures | gains when rates fall (lender) |
| Short futures | gains when rates rise (borrower) = long FRA (pay fixed) |
| BPV | notional × 0.0001 × period (3 months = 0.25, 1 month = 1/12) |
| Example | USD 1m, 3 months: USD 25. EUR 40m, 3 months: EUR 1,000 |
Memory hook Price up, rate down. A borrower hates higher rates, so a borrower sells the future.
Know it cold Linear: every basis point is worth the same BPV, up or down. Gain or loss = bp moved × BPV × contracts. 100 − rate is not a bond price.
- Gains when rates RISE Memorize price falls (100 − rate)
- Short rate futures hedges a future borrowing
- Long FRA pays fixed, receives floating
-
- Gains when rates FALL Memorize price rises (100 − rate)
- Long rate futures hedges a future deposit or lending
- Short FRA receives fixed, pays floating
-
Quick example
A three-month contract is quoted at 98.10. MRR = (100 − 98.10) ÷ 100 = 1.90%. A quote above 100 means a negative rate.
- 100−98.1= 1.9, so 1.90%
- 100ENTER98.1− 1.9, so 1.90%
ENTER enter (on the HP, puts the number on the stack)
Quick example
EUR 40 million on a three-month rate: 40,000,000 × 0.0001 × 0.25 = EUR 1,000 per basis point.
- 40000000×0.0001×0.25= 1000
- 40000000ENTER0.0001×0.25× 1000
ENTER enter (on the HP, puts the number on the stack)
Quick example
Long 12 contracts on GBP 4 million, three-month rate. The price falls from 98.40 to 98.20, which is −20 bp. BPV = GBP 100, so P&L = −20 × 100 × 12 = −GBP 24,000.
- 98.2−98.4=×100= -20 bp
- ×4000000×0.0001×0.25×12= -24000
- 98.2ENTER98.4−100× -20 bp
- 4000000×0.0001×0.25×12× -24000
ENTER enter (on the HP, puts the number on the stack)
How it is asked
-
Implied rate from a quote
A three-month future is quoted at 98.65. Implied rate?
100 − 98.65 = 1.35%. Traps: 100 ÷ 98.65 − 1 = 1.37% (a bond price), or × 4 = 5.40%.
-
BPV and gain or loss
Long 6 contracts, USD 1m, three-month, price 98.65 → 98.95.
30 bp × USD 25 × 6 = USD 4,500. Traps: one contract only; omitting the 0.25 period.
-
Hedge a future borrowing
Company borrows floating in two months and fears higher rates.
Sell rate futures (or buy an FRA). Trap: buying futures.
-
Equivalent FRA position
Which FRA position matches a long rate future?
Short FRA (receive fixed, pay floating): both gain when rates fall.
Exam traps
- Buying rate futures to hedge a future borrowing. A borrower sells them; the short gains when rates rise.
- Treating 100 − rate as the price of a zero-coupon bond. It is a quoting convention for a rate.
- Forgetting the period fraction in the basis point value (3 months is 0.25, not 1).
- Mixing up the FRA and futures sides. Long FRA = pay fixed = short futures.
- Mixing price points and basis points. One price point (1.00) is 100 basis points.
Checkpoint
6 exam-style questions. About 90 seconds each.
1A three-month interest rate futures contract is quoted at 97.15. The implied three-month rate is:
2An investor is long 10 three-month interest rate futures contracts of USD 1 million each. The price rises from 97.15 to 97.40. The gain is closest to:
3A company will borrow at a floating rate in two months and wants protection from rising rates. It should most appropriately:
4A bank is short 1 three-month interest rate futures contract on CAD 80 million. The reference rate rises 15 basis points. The bank's gain is closest to:
5A short-term interest rate futures contract trades at 100.20. The implied rate is:
6Which position gains when the market reference rate falls, like a long interest rate futures contract?
Key takeaways
- Price = 100 − rate, so price and rate move in opposite directions.
- Long futures gain when rates fall; short futures gain when rates rise, like a long (pay-fixed) FRA.
- BPV = notional × 0.0001 × period, and it is the same for every basis point.
- A borrower hedges by selling rate futures; a lender or depositor hedges by buying them.
Quick example
A three-month contract is quoted at 98.10. MRR = (100 − 98.10) ÷ 100 = 1.90%. A quote above 100 means a negative rate.
- 100−98.1= 1.9, so 1.90%
- 100ENTER98.1− 1.9, so 1.90%
ENTER enter (on the HP, puts the number on the stack)
Quick example
EUR 40 million on a three-month rate: 40,000,000 × 0.0001 × 0.25 = EUR 1,000 per basis point.
- 40000000×0.0001×0.25= 1000
- 40000000ENTER0.0001×0.25× 1000
ENTER enter (on the HP, puts the number on the stack)
Quick example
Long 12 contracts on GBP 4 million, three-month rate. The price falls from 98.40 to 98.20, which is −20 bp. BPV = GBP 100, so P&L = −20 × 100 × 12 = −GBP 24,000.
- 98.2−98.4=×100= -20 bp
- ×4000000×0.0001×0.25×12= -24000
- 98.2ENTER98.4−100× -20 bp
- 4000000×0.0001×0.25×12× -24000
ENTER enter (on the HP, puts the number on the stack)
All Derivatives formulas, every lesson
Practice exam-style questions on Pricing and Valuing Futures Contracts
Questions about this lesson?
Where this comes back
- Pricing and Valuing Interest Rate Swaps Derivatives
- Convexity and Portfolio Duration Fixed Income
- Introduction to Risk Management Portfolio Construction
Questions candidates ask
How are interest rate futures quoted?
As 100 minus the annualized reference rate in percent. A quote of 96.85 means 3.15%. The price moves opposite to the rate, and a quote above 100 means a negative rate. It is a quoting convention, not the price of a bond.
How do you calculate the basis point value of an interest rate future?
BPV = notional × 0.0001 × period, with the period in years. A USD 1 million contract on a three-month rate has a BPV of 1,000,000 × 0.0001 × 0.25 = USD 25. The value is the same for every basis point, up or down.
How do you hedge rising interest rates with futures?
Sell interest rate futures. The price, 100 minus the rate, falls when rates rise, so the short position gains and offsets the higher cost of floating-rate borrowing. A long (pay-fixed) FRA does the same job.
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