Cheapest to Deliver: The Bond Behind the Futures Price

Key Takeaways

• The short in a bond futures contract chooses which eligible bond to hand over, and always picks the cheapest to deliver, the bond that costs the least to buy relative to the invoice the exchange pays.
• The exchange assigns each deliverable a conversion factor to equalize coupons, but the adjustment is imperfect, so one bond is always slightly cheaper than the rest.
• The cheapest to deliver bond effectively sets the futures price and the contract's DV01, so its identity matters for both pricing and hedging.
• The cheapest to deliver can switch as yields move, and a mid-trade switch changes the contract's interest-rate sensitivity and can misweight a hedge.

What It Is

Physically settled bond futures, such as the CBOT Treasury complex now run by CME Group, do not reference a single security. The exchange publishes a basket of eligible bonds that satisfy the maturity and coupon rules for a given contract, and at delivery the short selects which one of those bonds to hand over.

Because the short gets to choose, it chooses the option worth the most money. The cheapest to deliver (CTD) is the eligible bond that produces the largest gain, or the smallest loss, when it is bought in the cash market and delivered against the futures. That bond, not the notional contract, is what the futures price actually reflects.

The Intuition

Every deliverable bond has a different coupon and maturity, so their cash prices differ widely. If the exchange simply demanded any bond, the short would always deliver the least valuable one. To prevent that, the exchange scales each bond by a conversion factor (CF) that adjusts for its coupon, quoting each as though it yielded the contract's notional 6 percent coupon.

The catch is that the conversion factor is only exact when a bond genuinely yields 6 percent. In the real world yields sit above or below that, so the scaling leaves small residual differences. Those residuals mean one bond is always marginally cheaper to deliver than the others, and the short zeroes in on it.

How It Works

When the short delivers, the long pays the invoice price:

invoice price = (futures settlement price x conversion factor) + accrued interest

To find the CTD, compare each bond's cash cost against that invoice. The standard screen is the gross basis, the cost of delivery ignoring financing:

gross basis = clean price - (futures price x conversion factor)

Accrued interest is paid when buying the bond and received in the invoice, so it cancels. The bond with the smallest gross basis is the cheapest to deliver. A more precise version, the net basis, also subtracts carry (coupon income minus repo financing) over the delivery window, but gross basis captures the core ranking.

There is a well-known bias. When market yields are above 6 percent, longer-duration, lower-coupon bonds tend to be cheapest to deliver. When yields are below 6 percent, shorter-duration, higher-coupon bonds tend to win. Because the futures price tracks the CTD almost one for one, the contract inherits the CTD's DV01, the dollar change in value per basis point of yield.

Worked Example

Suppose a Treasury futures contract settles at a price of 100.00, and three bonds are eligible for delivery:

Compute the gross basis for each, using gross basis = clean price minus (futures price times CF):

• Bond A: 98.50 - (100.00 x 0.9800) = 98.50 - 98.00 = 0.50
• Bond B: 102.00 - (100.00 x 1.0100) = 102.00 - 101.00 = 1.00
• Bond C: 95.20 - (100.00 x 0.9450) = 95.20 - 94.50 = 0.70

Bond A has the smallest gross basis, 0.50 per 100 of face, so Bond A is the cheapest to deliver. Note that Bond C is the lowest-priced bond outright, yet it is not the CTD. Raw price is irrelevant; what matters is price relative to the conversion-factor-adjusted invoice. The short delivers Bond A, and the futures price behaves as if it were a claim on Bond A.

Common Mistakes

1. Picking the lowest-priced bond. The cheapest to deliver is not the bond with the smallest cash price. It is the bond with the smallest gross basis, price relative to its conversion-factor-adjusted invoice, as Bond A versus Bond C shows above.
2. Treating the CTD as fixed. The cheapest to deliver can change when yields cross the 6 percent notional level or when the yield curve reshapes. A hedge built on the old CTD's DV01 quietly drifts off target.
3. Ignoring carry. Gross basis omits coupon income and repo financing. Over a long delivery window the net basis can reorder close candidates, so relative-value traders must include carry.
4. Misreading the conversion factor. A CF above 1 means the bond's coupon exceeds 6 percent, below 1 means it is under 6 percent. It is a scaling number, not a price or a probability.
5. Confusing invoice with market price. The long pays the invoice price, futures times CF plus accrued, not the bond's own quoted price. Sizing a delivery off the wrong figure produces a broken P&L.

Frequently Asked Questions

Q: What does cheapest to deliver mean in plain terms? Cheapest to deliver is the single bond, out of all the bonds eligible for a futures contract, that the short can buy and deliver for the smallest net cost. Because the short always picks it, that bond effectively determines the futures price.

Q: How is the cheapest to deliver bond actually identified? Compute the gross basis for every eligible bond, defined as its clean price minus the futures price multiplied by its conversion factor. The bond with the smallest gross basis is the cheapest to deliver. Traders refine this with net basis, which also accounts for carry.

Q: Why does the conversion factor exist? The conversion factor rescales each deliverable bond as if it yielded the contract's notional 6 percent coupon, so bonds with very different coupons can compete on a level footing. Because it is exact only at a 6 percent yield, small differences remain and one bond ends up cheapest.

Q: Can the cheapest to deliver bond change over time? Yes. As yields rise above or fall below 6 percent, or as the curve reshapes, a different bond can become cheapest. This CTD switch changes the contract's duration and DV01, which is why hedgers monitor it rather than assuming it is permanent.

Q: Does the cheapest to deliver affect the futures price? Directly. Since the short delivers the CTD, the futures price converges toward the CTD's price divided by its conversion factor, and the contract inherits the CTD's interest-rate sensitivity.

Sources

1. Investopedia. "Cheapest to Deliver (CTD)." https://www.investopedia.com/terms/c/cheapesttodeliver.asp
2. CME Group. "The Basics of U.S. Treasury Futures." https://www.cmegroup.com/trading/interest-rates/basics-of-us-treasury-futures.html
3. CME Group. "Treasury Futures Delivery Options, Basis Spreads, and Implied Repo Rates." https://www.cmegroup.com/education/files/treasury-futures-basis-spreads.pdf
4. CME Group. "U.S. Treasury Futures Conversion Factor Lookup Tables." https://www.cmegroup.com/trading/interest-rates/us-treasury-futures-conversion-factor-lookup-tables.html

Disclaimer

This article is educational content only and is not financial advice. Nothing here is a recommendation to buy, sell, or hold any security. Consult a licensed advisor before making investment decisions.