# Conversion factor Cheapest To Deliver Bond (CTD)

The conversion factor (CF) for the cheapest to deliver bond (CTD) is an important concept used to price fixed income futures. The conversion factor is needed to determine the principal invoice price. This is the price that the short party of a fixed income futures will receive upon settlement.

On this page, we discuss how to calculate the principal invoice price, the total invoice amount and the methods to identify the CTD bond. One of the two approaches uses the cash-and-carry model to price the future and determine the CTD bond.

# Conversion factor

The price of Treasury bond futures is based on a notional government bond. The notional government bond is assumed to have a coupon rate of 6%. Each eligible bond that can be delivered by the short party is assigned a conversion factor to reflect its value relative to the notional bond in the contract.

Conversion factors for eligible bonds are computed as the clean price of \$1 face value of the eligible bond discounted at a yield to maturity of 6%. As a consequence, bonds with a 6% coupon will have a CF of 6%, bonds with coupons higher than 6% will have CFs greater than 1, and bonds with a coupon less than 6% will have CFs less than 1.

The short party will receive the principal invoice price on delivery

In practice, the bond delivered may be between coupon dates at the delivery date, so the short party will also receive the accrued interest on the bond

## Cheapest-to-deliver-bond

The process to compute the CF is imperfect because it assumes a flat interest rate term structure. This bias in the computation of CFs means that one of the eligible bonds will generate the greatest gain (or smallest loss) to the short party at delivery. This bond is the cheapest-to-deliver-bond. This is the bond that will be used to price the future.

## Methods to determine the cheapest-to-deliver-bond

There are two methods to determine the cheapest-to-deliver bond.

• The first method identifies the eligible bond that generates the highest returns (implied repo rate on a cash-and-carry trade
• The second method is to find the eligible bond with the lowest basis (basis is defined as the spot price minus the futures price).

The treasury with the lowest basis will typically have the highest implied repo rate and will be the cheapest to deliver.

## Summary

We discussed the conversion factor and the cheapest-to-deliver (CTD) bond. These concepts are used when pricing fixed income futures.