Calculating U.S. Treasury Futures Conversion Factors
Each cash note or bond eligible for delivery into a Treasury futures contract is assigned a conversion factor, which considers its coupon and the time remaining until maturity as of a specific delivery month. The conversion factor represents the estimated decimal price at which $1 par value of the security would trade if it had a yield to maturity of 6%.
The conversion factor serves a pragmatic role by standardizing the valuation of deliverable securities. It represents an estimated price at which the bond or note would trade, assuming a 6% yield to maturity. Throughout a specific delivery cycle, conversion factors remain consistent and act as a multiplier in determining the invoice prices for securities delivered within the futures contract.
In cases where the coupon exceeds 6%, the conversion factor is greater than 1, reflecting the higher relative value of the security. Conversely, if the coupon falls below 6%, the conversion factor is less than 1, indicating a comparatively lower value for the security.
Conversion factors for currently listed Treasury futures are listed are published in accordance with the Treasury’s Tentative Auction Schedule.
The cheapest-to-deliver security can be found on the CME Group Treasury Analytics tool.
Exhibit 1: Deliverable grades for Treasury futures
The formula for calculating a conversion factor1 is:
where the factor is rounded to four decimal places. And:
coupon is the bond or note’s annual coupon in decimals rounded to the nearest one-eighth of one percent (rounded up in the case of ties).
n is the number of whole years from the first day of the delivery month to the maturity (or call) date of the bond or note.
z is the number of whole months between n and the maturity (or call) date rounded down to the nearest quarter for UB, ZB, TWE, TN and ZN, and to the nearest month for ZF, Z3N, and ZT
The first step in calculating the conversion factor is to determine how many months there are until the first coupon payment, where v is used as a helper:
Coupons for Treasury notes and bonds are paid on a semiannual basis. For the contracts with a three-month rounding convention, z can equal 0, 3, 6, 9. If the value of z = 3 or 9, then there is 3 months until the next coupon payment. If the value of z = 0 or 6, then there is 6 months until the next coupon payment.
For contracts with a one-month rounding convention, z can equal any value from 0 to 11. If z ≥7, then we subtract 6 to change v to a half year increment, which will assist in calculating the number of months until the next coupon payment in b.
Component a of the conversion factor formula is simply a present value formula:
The FV in the equation is the face value of the bond or note, $100 or 1, and r represents the assumed yield maturity of 6%, or 3% due to the semiannual coupon payments. v and a have an inverse relationship. As v increase, or gets further from the next coupon payment, the value of a decreases.
Component b discounts the coupon based on how many months there are until the next coupon payment. Since payments are semiannual, the coupon is divided by 2, and then it is discounted. If v=0, then there is 6 months until the next coupon, indicating a discount factor of 1, resulting in b=coupon/2. If v=6 then there are 0 months until the next coupon, so the discount factor is 0, resulting in b=0.
Component c is also a present value formula like component a. Component c counts the number of semi-annual coupon payments there will be. If z < 7, then the first coupon payment of the year has not occurred yet, therefore the number of coupon payments is similar the number of years multiplied by 2. If z ≥ 7, then the first coupon payments have already occurred for the current year, thus another coupon payments must be added to accommodate for second payments of the year.
Component d adjusts the magnitude of the coupon of the U.S. Treasury security. This is done to equalize the securities in a deliverable basket. If all conversion factors were set to 1, then the security with the lowest issued coupon would always the cheapest to deliver. To avoid this, Component d is scaled by component c to tune the impact of the coupons.
1 - The conversion factor for any note shall be the price at which it will yield six percent (rounded to four decimal places) based on the formula found in Standard Securities Calculation Methods published by the Securities Industry Association.
2-Year U.S. Treasury Note futures contract (ZT/26)
Calculate the conversion factor for the 5s of September 30, 2025, (i.e., 91282CJB8) for the December 2023 expiry.
The first day of the December 2023 delivery month is Friday, December 1, 2023.
Remaining term to maturity of 1 year, 9 months based upon an actual remaining maturity of 1 year 9 months and 29 days. Notice that the remaining term to maturity for ZT rounds down in one-month increments. Therefore:
3-Year U.S. Treasury Note futures contract (Z3N/3YR)
Calculate the conversion factor for the 4 5/8s of November 15, 2026, (i.e., 91282CJK8) for the December 2023 expiry.
The first day of the December 2023 delivery month is Friday, December 1, 2023.
Remaining term to maturity of 2 years, 11 months based upon an actual remaining maturity of 2 year 11 months and 14 days. Notice that the remaining term to maturity for Z3N rounds down in 1-month increments. Therefore:
