Cheapest to Deliver (CTD) Explained: Definition, Formula, and Examples
What is Cheapest to Deliver (CTD)?
Cheapest to Deliver (CTD) is the deliverable security that minimizes the short seller’s cost when fulfilling a futures contract that allows multiple possible deliverable instruments. It’s most commonly referenced in Treasury bond futures, where several bonds may meet contract specifications (maturity window, coupon range, etc.). The short party chooses which eligible bond to deliver; the bond that yields the lowest net delivery cost is the CTD.
Why CTD matters
- CTD influences futures pricing and the basis between futures and cash bond markets.
- Shorts choose the CTD to maximize profit or minimize delivery cost.
- Market participants and exchanges monitor CTD when assessing hedging and arbitrage opportunities.
Key formulas and concepts
-
Invoice price (what the short receives at delivery):
Invoice = Futures settlement price × Conversion factor + Accrued interest -
Gross basis (simple measure used to compare deliverables):
Gross basis = Market (clean) bond price − (Futures settlement price × Conversion factor)
The CTD is the bond with the lowest gross basis (i.e., the most negative or smallest value), because that bond is cheapest for the short to acquire/hold relative to what the short will be paid upon delivery.
Explore More Resources
-
Implied repo rate (more comprehensive metric):
The implied repo rate is the return a trader would earn by buying the bond, shorting the futures, and holding to delivery (it implicitly reflects financing/carry costs). A higher implied repo indicates a cheaper-to-deliver characteristic after accounting for cost of carry and financing. -
Conversion factor:
Exchanges calculate conversion factors to normalize bonds of different coupons and maturities so they can be compared as deliverables. The conversion factor roughly adjusts the futures invoice price to reflect differences in coupon and maturity.
How to determine CTD — step-by-step
- For each eligible bond, obtain:
- Market clean price (excluding accrued interest)
- Conversion factor
- Futures settlement price
- Accrued interest (if you want invoice-level comparisons)
- Compute the invoice price for each bond:
Invoice = Futures settlement price × Conversion factor + Accrued interest - Compute the gross basis for each bond:
Gross basis = Market clean price − (Futures settlement price × Conversion factor) - The CTD is the bond with the lowest gross basis (or, if using implied repo, the bond with the highest implied repo).
Numerical example
Assume futures settlement price = 100.
-
Bond A: market price = 102, conversion factor = 1.02
Invoice = 100 × 1.02 = 102
Gross basis = 102 − 102 = 0 -
Bond B: market price = 101, conversion factor = 1.00
Invoice = 100 × 1.00 = 100
Gross basis = 101 − 100 = 1 -
Bond C: market price = 99, conversion factor = 1.02
Invoice = 100 × 1.02 = 102
Gross basis = 99 − 102 = −3
Here, Bond C has the lowest gross basis (−3), so it is the CTD: it is cheapest for the short to deliver.
Practical considerations
- Accrued interest matters if comparing invoice amounts rather than clean prices.
- Implied repo incorporates financing costs and may change the CTD ranking relative to the gross basis.
- Exchanges periodically update conversion factors to reflect bond characteristics; CTD can shift as market prices and yields move.
- CTD is a dynamic outcome—changes in yield curve, supply/demand, and financing rates can change which bond is CTD.
Bottom line
Cheapest to Deliver identifies the most cost-effective deliverable security for a short position in a futures contract. Use the invoice and gross-basis calculations (or implied repo for a carry-adjusted view) to compare eligible bonds. Understanding CTD helps traders anticipate delivery choices, evaluate basis risk, and design arbitrage or hedging strategies.