How CTD Conversion Factors Scale Futures Duration

Summary

The document explains why a Treasury futures duration estimate based on the cheapest-to-deliver bond is divided by that bond’s conversion factor. First, estimate the CTD bond’s duration in forward space using the futures delivery date as settlement and the invoice price as the bond price. Then scale that duration by the conversion factor to approximate how sensitive the futures price is to changes in the CTD bond’s yield.

The rationale is that futures price is approximately the CTD bond’s clean price divided by its conversion factor, with carry and embedded optionality also affecting the relationship. The response gives an intuition based on bond price sensitivity, but it does not derive the approximation or quantify its accuracy. It assumes there is no delivery switch risk, and the estimate may be less reliable when carry or delivery optionality has a material effect.

Key ideas

• A bond’s duration measures how its price responds approximately to yield changes.
• The CTD bond’s duration can be estimated in forward space using the delivery date and invoice price.
• Dividing CTD duration by its conversion factor approximates futures price sensitivity to the CTD yield.
• Carry and delivery optionality can make the approximation less accurate.

Tags

# Duration of a futures contract


# Duration of a futures contract












I have tried to find an answer to this question but have come up with nothing.

So, it is my understanding that to find the duration of a futures contract (assuming no switch risk), all you need to do is find the duration of the CTD in the forward space (by using the delivery date as the settlement date, and by using the invoice price as the price of the CTD), and divide the duration of the CTD by its conversion factor. My questions is, what is the mathematical rationale for dividing the duration of the CTD by its conversion factor, when you are already adjusting the price of the CTD for the conversion factor?

## Answer by GZ- (score 1)

https://quant.stackexchange.com/a/66015

By dividing the duration of the CTD by its conversion factor, we arrive at a number that approximates the sensitivity of the futures price to the yield of the CTD.

Recall that duration of a bond is a measure of its price sensitivity to the change in its yield. Since Futures price is approximately the CTD bond (clean) price divided by the conversion factor (minus carry and any value from its optionality), dividing the duration of the CTD by the conversion factor gives you approximate price sensitivity of the futures to the yield of the CTD.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.