Cheapest to Deliver (Futures)
The cheapest to deliver (CTD) bond is the specific Treasury security from the deliverable basket that maximizes the net proceeds to the short futures position holder when physically settling a Treasury futures contract, making it the rational choice for delivery and the primary determinant of futures pricing.
Treasury futures contracts — including the 2-year, 5-year, 10-year, and Ultra 10-year, Long Bond, and Ultra Long Bond contracts traded on the CME Group — are physically settled instruments. When a futures position is held to expiration, the short (seller) of the futures contract must deliver an eligible Treasury security to the long (buyer). Because multiple Treasury securities qualify for delivery under each contract, the short has the option of choosing which eligible bond to deliver — and will rationally choose the one that is cheapest for them to deliver.
The cheapest to deliver is not necessarily the bond with the lowest market price. Instead, it is the bond that maximizes the profit (or minimizes the loss) for the short when adjusted for the conversion factor applied under the futures settlement rules. The net proceeds received by the short from delivering a specific bond are: Net Proceeds = Futures Settlement Price x Conversion Factor + Accrued Interest. The short then compares these proceeds against the cost of purchasing the bond in the spot market: Cost = Clean Price + Accrued Interest. The bond with the highest value of (Proceeds - Cost) is the CTD.
The CTD bond changes over time based on several factors, primarily the level of interest rates and the shape of the yield curve. At low yield levels, long-duration bonds within the deliverable basket tend to be CTD because their conversion factors, which are computed assuming a 6% notional coupon, overestimate their actual value, making them relatively cheap to deliver. At high yield levels, low-duration bonds near the 6% coupon assumption tend to become CTD.
Futures prices are anchored to the CTD bond because arbitrage keeps the relationship tight. The theoretical futures price is approximately: Futures Price = (CTD Spot Price - Carry) / Conversion Factor, where carry reflects accrued interest and repo financing costs over the futures delivery period.
For portfolio managers, identifying the CTD bond matters for hedging. A Treasury futures hedge is effectively a hedge of the CTD bond, not a hedge of the entire portfolio. If the portfolio holds securities that differ from the CTD in duration, coupon, or maturity, basis risk exists between the portfolio and the futures hedge. Risk managers must account for the possibility that the CTD bond switches to a different security, which can introduce sudden changes in hedge effectiveness and futures pricing.