Cheapest-to-Deliver
The cheapest-to-deliver (CTD) bond is the Treasury bond or note that a short futures position holder would find most economical to deliver to satisfy a maturing Treasury futures contract, determined by comparing the cost of purchasing a deliverable bond versus the invoice price received from the long.
Key takeaways
- CTD is identified by minimizing the Delivery Cost: CTD = argmin [Clean Price of Bond − (Futures Price × Conversion Factor)].
- Conversion factors (CF) standardize deliverable bonds to approximate the 6% notional coupon of the futures contract, but imperfect standardization creates CTD optionality for the short position.
- The CTD bond changes as yields fluctuate: low-coupon, long-duration bonds tend to be CTD in low yield environments; high-coupon, short-duration bonds become CTD when yields are high.
- The short position's embedded delivery option (quality option) has value because the short can switch to a different deliverable bond throughout the delivery month if that becomes cheapest.
- Treasury futures prices are approximately: Futures Price ≈ (CTD Bond Price − Accrued Interest) / Conversion Factor, adjusted for carry and the delivery option premium.
Explanation
Treasury bond and note futures (T-Bond, 10-year, 5-year futures) do not require delivery of a single specific bond. Instead, they allow delivery of any qualifying Treasury bond within a defined maturity and coupon range. This flexibility is designed to prevent short squeezes but creates the CTD phenomenon: rational short position holders will deliver whichever eligible bond costs them the least, after adjusting for the conversion factor (which normalizes different coupons and maturities to a standardized 6% coupon bond).
The conversion factor (CF) is a scaling factor applied to each deliverable bond, calculated by the exchange as the price of the bond per $1 face value if it were to yield exactly 6%. The invoice price received by the short on delivery is: Invoice Price = Futures Settlement Price × CF × Face Value + Accrued Interest. The short's net profit/loss from delivering a specific bond is: P&L = Invoice Price − (Clean Bond Price × Face Value + Accrued Interest). The CTD is the bond that maximizes this P&L (or equivalently, minimizes the net cost to the short).
The CTD mechanism creates a yield-dependent switching behavior. In a low yield environment (below 6%), long-duration bonds have prices well above par; the conversion factor system slightly undervalues them (because CF assumes 6% yield). Therefore, high-duration bonds appear cheap relative to their CF-adjusted invoice price, and the CTD tends to be the bond with the longest duration (most DV01 per unit of invoice price). When yields rise above 6%, the conversion factor slightly overvalues high-coupon/short-duration bonds, making them the CTD. This duration shift in the CTD is crucial for the futures contract's effective DV01 and its suitability as a hedge.
The embedded quality option is the short's right to deliver any eligible bond. The value of this option increases with: (1) yield curve steepness (greater differences between bonds' prices); (2) yield volatility (more likely to cross the CTD switching point); and (3) the number of eligible deliverable bonds (more candidates means more potential switches). Market participants use term structure models to value this option, which explains why Treasury futures prices trade at a discount to the theoretical no-option price — the futures are 'cheap' by approximately the option value.
For portfolio managers using Treasury futures to hedge duration, the CTD identification is essential for accurate DV01 calculation. The futures contract's DV01 ≈ CTD DV01 / CF. If the CTD switches (due to yield movements), the hedge ratio must be recalculated immediately. Basis trading — taking simultaneous positions in a specific deliverable bond and the futures contract — exploits anticipated CTD changes or carries the bond through delivery while collecting the 'carry and roll' premium.
Formula
CTD = Bond with minimum [Clean Price − Futures Price × Conversion Factor]; Invoice Price = Futures Price × CF + Accrued Interest
Example
Treasury 10-year futures trade at 112-16 ($112.50 per $100 face value). Three eligible deliverable bonds are analyzed. Bond A: 2.875% coupon, 9.5 years to maturity, clean price $98.50, CF = 0.8765. Bond B: 4.125% coupon, 10.2 years to maturity, clean price $103.75, CF = 0.9225. Bond C: 1.625% coupon, 9.8 years to maturity, clean price $91.25, CF = 0.8112. Delivery cost for Bond A: $98.50 − (112.50 × 0.8765) = $98.50 − $98.61 = −$0.11 (benefit). Bond B: $103.75 − (112.50 × 0.9225) = $103.75 − $103.78 = −$0.03 (slight benefit). Bond C: $91.25 − (112.50 × 0.8112) = $91.25 − $91.26 = −$0.01. Bond A has the lowest net delivery cost (most negative = most beneficial for the short), making it the CTD. The futures contract's duration and DV01 should be calculated using Bond A's characteristics.
Related terms
Accrued Interest Basis Bond Clean Price Delivery Duration Dv01 Exchange Face Value Floating Rate Note Futures Contract Hedge Ratio