Cheapest to Deliver (CTD)
The specific deliverable bond a short Treasury-futures holder will choose to deliver because it is the least costly to source net of the invoice received.
Formula
Net Cost to Deliver = Bond Price − (Futures Price × Conversion Factor); CTD minimizes this
Cheapest to deliver (CTD) is the security a short futures holder picks to satisfy delivery when a contract permits a basket of eligible underlyings. It matters most in Treasury futures, where the seller may deliver any of several eligible government bonds within a maturity window. The short, holding the delivery option, naturally delivers whichever bond costs the least to buy relative to the cash they receive.
The exchange adjusts each eligible bond's invoice price by a conversion factor that normalizes coupons and maturities to a notional standard (for CME Treasury futures, a 6% notional coupon). The CTD is the bond that minimizes Net cost = Bond Price − (Futures Price × Conversion Factor) — essentially the smallest gross basis (precisely, the bond with the highest implied repo rate). Because the front future tracks this bond, the CTD effectively defines the future's price behavior, duration, and DV01.
The CTD is not fixed: as yields move across the 6% notional pivot, the cheapest bond can switch between low-coupon/long-duration and high-coupon/short-duration issues. Traders running basis or duration hedges must monitor for a CTD switch, because it abruptly changes the future's interest-rate sensitivity.
Example
Two eligible bonds for a 10-year note future priced at 110.00. Bond A: price 98.50, conversion factor 0.8900 → net cost = 98.50 − (110.00 × 0.8900) = 98.50 − 97.90 = 0.60. Bond B: price 98.00, conversion factor 0.8800 → net cost = 98.00 − (110.00 × 0.8800) = 98.00 − 96.80 = 1.20. Bond A has the smaller positive net cost, so Bond A is cheapest to deliver.
Related Terms
Basis (Futures)
The price difference between the spot (cash) price of an underlying and its corresponding futures price.
IntermediateBasis Convergence
The tendency of a futures price and its underlying spot price to meet as expiration nears, forcing the basis to zero at settlement.
IntermediateDuration
A measure of a bond's sensitivity to interest rate changes — the approximate percentage price change for a 1% move in yield.
AdvancedPhysical Delivery
Settlement method where the seller of a futures contract must deliver the actual underlying commodity to the buyer at expiration.
IntermediateTreasury Futures
CBOT futures on US government bonds — including 2-year, 5-year, 10-year notes and 30-year bonds — used to trade interest rate risk.
Intermediate