FRM Exam Part I · Interest Rate Futures

Treasury Bond and Note Futures: Conversion Factor and CTD

Updated 11 October 2026 · Fact-checked

Treasury bond and note futures let the short deliver any eligible bond. The conversion factor adjusts each bond to a common 6% yield. Cash received = (quoted futures price × conversion factor) + accrued interest. The cheapest-to-deliver bond minimises quoted bond price minus (futures price × conversion factor).

Understand Treasury Bond and Treasury Note Futures

A Treasury futures contract is an agreement to deliver a US Treasury bond or note in the future. Unlike a simple forward, the contract does not name one bond. The short position can choose from a basket of eligible bonds with different coupons and maturities. This creates the need for a fair way to compare them.

The conversion factor does this. It is the price of the delivered bond per $1 of face value if it were priced at a 6% yield (semiannual compounding), with maturity rounded down to the nearest three months. A bond with a coupon above 6% has a factor above 1. A bond with a coupon below 6% has a factor below 1. The short receives the quoted futures price times the conversion factor, plus accrued interest, for each $100 of face value.

Because the conversion factor is only an approximation, one bond is usually cheaper to deliver than the others. This is the cheapest-to-deliver (CTD) bond. The short buys it in the market at its quoted price and delivers it, receiving futures price × conversion factor. So the cost of delivery is quoted bond price minus (futures price × conversion factor). The bond with the lowest cost is the CTD. Accrued interest is paid by the long on the delivered bond, so it cancels and you compare quoted prices only.

The short also holds delivery options. The quality (switch) option is the choice of which bond to deliver. The timing option is the choice of which day in the delivery month. The wild card option is the right to give notice of delivery after the futures market closes, usually 2pm, while the invoice price is fixed at the close. These options favour the short, so they lower the futures price.

When yields are above 6%, the CTD tends to be a low-coupon, short-maturity bond. When yields are below 6%, it tends to be a high-coupon, long-maturity bond. These are rules of thumb. Always confirm with the cost calculation. To price the contract once the CTD is known, treat it as a forward on that bond, and divide by the conversion factor.

Key formulas to remember

Cash received by short: Cash = (Quoted futures price × Conversion factor) + Accrued interest; Per $100 face value. The long pays this invoice amount.
Cost of delivery: Cost = Quoted bond price − (Quoted futures price × Conversion factor); Choose the bond with the lowest cost as CTD. Ignore accrued interest, which cancels.
Conversion factor: CF = price of the bond at a 6% yield (semiannual), per $1 face, using maturity rounded down to the nearest 3 months; Coupon above 6% gives CF above 1. Coupon below 6% gives CF below 1.
Quoted futures price from CTD: Quoted futures price = (Forward cash price of CTD − Accrued interest at delivery) ÷ CF; Forward cash price = (Spot cash price − PV of coupons) × e^(rT), under continuous compounding.
Accrued interest: Accrued = Coupon ÷ 2 × (days since last coupon ÷ days in coupon period); Treasury bonds use actual/actual day count.

How to solve Treasury Bond and Treasury Note Futures questions

Follow the same order for any question on Treasury futures delivery or pricing.

1Identify what is asked: invoice amount, CTD bond, or futures price.
2List each deliverable bond with its quoted price, coupon and conversion factor.
3For each bond, compute quoted price − (futures price × CF).
4Pick the lowest result as the CTD. Check that it makes sense given whether yields are above or below 6%.
5For an invoice amount, compute futures price × CF and add accrued interest at delivery, scaled to the contract size.
6For futures pricing, find the CTD's forward cash price, subtract accrued interest at delivery, then divide by the CF.
7Check that the answer is per $100 face, then scale for a contract size of $100,000.

Quickest way: Fast CTD screen

When to use it: Use it when the question gives several bonds and a futures price and asks for the CTD.

Multiply the futures price by each CF in your head or on the calculator.
Subtract from each bond's quoted price.
The smallest difference wins. Ignore accrued interest.
Sanity check: yields above 6% point to low coupon, short maturity bonds.

Common mistakes in Treasury Bond and Treasury Note Futures

Adding accrued interest when comparing bonds for the CTD.
Students confuse the invoice price with the cost comparison.
Fix: Accrued interest is paid by the long on whichever bond is delivered, so it cancels. Compare quoted price − futures price × CF.
Choosing the CTD as the bond with the lowest quoted price.
It feels intuitive to pick the cheapest bond.
Fix: Cheapest means lowest net cost after the CF-adjusted futures receipt. Always do the subtraction.
Dividing the futures price by the conversion factor when computing invoice cash.
Mixing up the invoice formula with the futures pricing formula.
Fix: Invoice uses multiplication by CF. Dividing by CF is only used when backing out the futures price from the CTD's forward price.
Forgetting that the delivery options lower the futures price.
Students treat the contract as a plain forward.
Fix: The options belong to the short, so the long pays less for the contract. The futures price is below the plain forward-based value.
Using the CTD rule of thumb as always true.
The yield-vs-6% rule is memorised as a law.
Fix: It is a tendency. If numbers are given, calculate.

Worked examples

Example 1

Futures quoted price is 120. Three deliverable bonds: A quoted 125.00, CF 1.0400; B quoted 140.00, CF 1.1800; C quoted 98.00, CF 0.8200. Which is the CTD?

Show the solution

A: 125.00 − (120 × 1.0400) = 125.00 − 124.80 = 0.20.
B: 140.00 − (120 × 1.1800) = 140.00 − 141.60 = −1.60.
C: 98.00 − (120 × 0.8200) = 98.00 − 98.40 = −0.40.
The lowest cost is B at −1.60.

Answer: Bond B is the CTD, with a cost of −1.60 per $100 face.

Example 2

A Treasury bond futures contract is settled with a bond that has CF 1.2000. The quoted futures price is 95 and accrued interest on the bond is 2.50 per $100 face. What cash does the short receive for $100,000 face?

Show the solution

Quoted futures price × CF = 95 × 1.2000 = 114.00.
Add accrued interest: 114.00 + 2.50 = 116.50 per $100 face.
Scale to $100,000 face: 116.50 × 1,000 = $116,500.

Answer: The short receives $116,500.

Exam tips

Questions often hand you a table of bonds. Do the subtraction for each and pick the minimum.
Know which direction the delivery options move the futures price: down, because they favour the short.
Remember that the wild card option is about timing after the market close, and the quality option is about the choice of bond.
Read whether the price given is quoted or cash. Convert before you compare.
Watch units: price is per $100 face, contract is $100,000 face.

Practice questions from Interest Rate Futures

Treasury Bond and Treasury Note Futures: frequently asked questions

What is the conversion factor in Treasury futures?

It is the price of the deliverable bond per $1 of face value at a 6% yield, with semiannual compounding and maturity rounded down to the nearest three months. It puts all deliverable bonds on a comparable basis.

How do you find the cheapest-to-deliver bond?

For each bond, compute quoted bond price minus (quoted futures price × conversion factor). The bond with the lowest value is the CTD. Accrued interest is ignored because it cancels.

What is the wild card option?

It lets the short give notice of delivery after the futures market closes, while the invoice price is set at the close. If the bond price falls after the close, the short can profit by buying and delivering at the fixed invoice price.

Do the delivery options raise or lower the futures price?

They lower it. The options benefit the short, so the long should pay less to enter the contract.