A bond conversion factor is the multiplier the exchange assigns to each Treasury security eligible for delivery against a Treasury futures contract, and it puts every deliverable bond on a common pricing footing. Numerically, it is the clean price of one dollar of par value of that bond calculated at a 6 percent yield to maturity.1CME Group. Calculating U.S. Treasury Futures Conversion Factors You use it in two places: the invoice price the buyer pays when a bond is delivered, and the analysis that identifies the cheapest bond to deliver.
Why the Factor Exists
Treasury futures are written against a hypothetical bond with a 6 percent coupon that doesn’t trade in the cash market. Dozens of real Treasuries qualify for delivery against a single contract, and they carry different coupons and maturities that make their prices vary widely. Without an adjustment, sellers would always deliver whichever bond happened to be cheapest, and buyers would receive unpredictable value.2CME Group. Understanding Treasury Futures
Conversion factors scale the futures price up or down by each deliverable bond’s characteristics. A bond with a coupon above 6 percent gets a factor greater than one, so the buyer’s invoice price rises. A bond with a coupon below 6 percent gets a factor less than one, so the invoice price falls.2CME Group. Understanding Treasury Futures The system makes all eligible bonds roughly equivalent for delivery. “Roughly” does real work in that sentence, because a flat 6 percent assumption never matches actual market yields, and that imperfection is what creates the cheapest-to-deliver phenomenon.
How the Factor Is Calculated
The conversion factor equals the clean price (excluding accrued interest) of one dollar face value of the bond, discounted at a 6 percent annual yield compounded semiannually, as of the first day of the delivery month.1CME Group. Calculating U.S. Treasury Futures Conversion Factors In practice, that means taking every remaining coupon payment and the final principal repayment, discounting each one back at 3 percent per semiannual period, and summing them.
Before running the math, the exchange rounds the bond’s remaining maturity down to the nearest three-month increment. Two bonds maturing a few weeks apart can therefore share the same factor. The exchange computes and publishes all conversion factors before the contract begins trading, and the values stay fixed throughout the delivery month.2CME Group. Understanding Treasury Futures
A simplified example: a Treasury bond pays a 4 percent annual coupon (2 percent semiannually) with exactly 20 years remaining as of the first day of the delivery month. Its conversion factor is the present value of 40 semiannual payments of $0.02 plus the $1 principal, all discounted at 3 percent per period. That works out to roughly 0.77, reflecting the fact that a 4 percent coupon is worth less than the 6 percent standard. The buyer’s invoice would scale down accordingly.
Which Bonds a Factor Applies To
Not every outstanding Treasury is eligible. Each futures contract defines a maturity window measured from the first day of the delivery month, and a bond that falls outside the window by even a day is out of the basket. The 2-year note contract requires one year and nine months to two years remaining; the 5-year requires at least four years and two months (with original maturity capped at five years and three months); the 10-year requires at least six and a half but less than eight years; the 20-year bond requires between 19 years and two months and 19 years and 11 months; the classic U.S. Treasury Bond contract takes 15 to under 25 years; and the Ultra T-Bond takes 25 years or more.3CME Group. The Treasury Futures Delivery Process4CME Group. Chapter 25 – 20-Year U.S. Treasury Bond Futures The wider the window, the more bonds enter the deliverable basket, which is why the cheapest-to-deliver analysis is most complex for the long-bond and Ultra contracts.
Using the Factor to Compute the Invoice Price
When a seller delivers a bond, the buyer pays an invoice price given by:
Invoice Price = (Futures Settlement Price × Conversion Factor) + Accrued Interest
The futures settlement price is the exchange’s final daily settlement. Multiplying by the conversion factor adjusts that standardized price to the specific bond being delivered.1CME Group. Calculating U.S. Treasury Futures Conversion Factors Accrued interest compensates the seller for coupon income earned between the last coupon date and delivery, calculated on Treasuries with an actual/actual day count rather than the simplified 30-day-month assumption used for corporate bonds.5U.S. Department of the Treasury. Interest Rates – Frequently Asked Questions On large deliveries, a few miscounted days can meaningfully change the amount that changes hands.
Using the Factor to Find the Cheapest-to-Deliver Bond
The cheapest-to-deliver (CTD) bond is the security a seller can buy in the cash market and deliver against the futures contract at the lowest net cost, or the greatest profit. Because conversion factors are fixed while market prices move constantly, some eligible bonds are more economical to deliver than others. Identifying which one starts with gross basis:
Gross Basis = Cash Price – (Futures Price × Conversion Factor)
A lower gross basis means the bond is closer to being deliverable at a profit.6CME Group. The Basics of Treasuries Basis Gross basis ignores carry, meaning the coupon income the seller earns minus the financing cost of holding the bond until delivery. Net basis strips out carry and gets closer to the true delivery economics. The most precise measure is the implied repo rate, which is the annualized return from buying the bond, selling futures, and delivering at expiration. The bond with the highest implied repo rate is the cheapest to deliver, because it offers the best return on the cash-and-carry trade.
Because prices move all day and the basket can hold a dozen or more securities, institutional desks generally rely on software that recalculates implied repo rates in real time. Even small yield moves can switch the CTD from one bond to another.
How Rate Moves Bias the CTD
The conversion factor system works cleanly only at exactly 6 percent. At any other yield, the fixed factors create a systematic bias. When market yields rise above 6 percent, longer-duration bonds (low coupons, long maturities) become the CTD: their prices drop more sharply than short-duration bonds while their factors stay the same, so delivery cost falls relative to the invoice received. When yields fall below 6 percent, the CTD shifts toward shorter-duration, higher-coupon bonds for the mirror reason. At yields close to 6 percent, the CTD can flip between bonds on small daily moves, making basis trades particularly volatile.
Delivery Timing That Affects the Trade
Two features of the delivery mechanics interact with the conversion factor and matter for anyone using it in a trade.
First, the delivery window itself. Delivery follows a three-day sequence set by the CBOT under CFTC oversight: intention day, invoice day, and delivery day, with the short’s clearing firm notifying CME Clearing of intent by 6:00 p.m. CT on day one and securities transferring by 1:00 p.m. CT on day three.3CME Group. The Treasury Futures Delivery Process Any short position still open after the last intention day is automatically taken through delivery; there is no offset at that point.
Second, the wild card option. The exchange publishes each day’s futures settlement shortly after 2:00 p.m. CT, but the short has until 6:00 p.m. CT to declare intent to deliver, while cash Treasury prices keep moving until roughly 4:30 p.m. CT.7CME Group. Treasury Futures Delivery Options, Basis Spreads, and Delivery Tails If cash prices drop sharply in that window, the seller can buy bonds cheaper and deliver them against the already-fixed invoice amount. That optionality is one reason Treasury futures tend to trade at a slight discount to the theoretical fair value implied by the CTD bond alone.
Tax Treatment of the Result
Treasury futures are Section 1256 contracts under federal tax law. Open positions are marked to market at year end, meaning the IRS treats them as sold at fair market value on the last business day of the tax year whether or not the trader closed them. Gains and losses receive the 60/40 split: 60 percent long-term and 40 percent short-term, regardless of actual holding period.8Office of the Law Revision Counsel. 26 U.S. Code 1256 – Section 1256 Contracts Marked to Market For traders in higher brackets, the blended rate is lower than the short-term rate that would otherwise apply, and losses accrue in the year they arise even on positions still open.