How Conversion Factors Standardize Treasury Bond Futures Deliverables
Summary
Conversion factors make bonds with different coupons and prices comparable in a futures contract that accepts multiple deliverable securities. The explanation starts with the cheapest-to-deliver problem: if futures settlement simply tracked one bond’s forward price, bonds with differing coupons would not be treated consistently, and the lowest-priced deliverable could dominate.
The proposed standard is each bond’s price at a chosen reference yield, illustrated with a 6% nominal coupon assumption. Multiplying the futures price by a bond’s conversion factor sets its invoice value, allowing deliverables to be compared on that basis. The document then describes the exchange formula as a practical approximation to valuing bonds at that reference yield, with adjustments for fractional coupon periods. It is an intuition-focused explanation rather than a derivation of the formula; the reference coupon is described as an arbitrary convention, and the example does not address other contract or delivery details.
Key ideas
- Conversion factors put bonds with different coupons on a common pricing basis for delivery.
- A basket of deliverable bonds creates a cheapest-to-deliver consideration.
- The factor can be understood as the bond’s price at a chosen reference yield.
- The 6% reference coupon is a convention, not a forecast of market yields.
- The exchange formula approximates standardized bond pricing while handling fractional coupon periods.
Tags
Full text
# Intuition behind Conversion Factor, Bond Future
# Intuition behind Conversion Factor, Bond Future
My question is, how did people first come up with this formula?
$$CF = a (\frac{coupon}{2}+c+d)-b$$
Where $a,b,c,d$ are further defined as (strange looking) nonlinear functions of the bond's parameters.
How did they derive it? How do you go from these formula to the intuition of 6% in the end?
Computation method: https://www.cmegroup.com/trading/interest-rates/files/Calculating_U.S.Treasury_Futures_Conversion_Factors.pdf
## Answer by Attack68 (score 3)
https://quant.stackexchange.com/a/80517
Imagine wanting to create a deliverable bond future tradable on an exchange. We define which single bond is deliverable to it and use the forward price of the bond as the basis for the future. This works fine. I believe this is how Swedish government bond futures work.
Someone now suggests that there should be more than one deliverable bond into the futures contract. There is now a potential basket. An astute trader makes the point that some bonds will always have a higher price than others based on their coupon. If the future is just a forward price of one of those bonds it will always be of the bond with the lowest price (this is the cheapest to deliver); this makes no sense.
The suggestion is to standardise all the bonds in the basket to make them comparable. If the nominal coupon on the future is (arbitrarily) 6% then whatever price each bond has with a YTM of 6% acts as the conversion factor. If the futures price is 100 then multiplied by each bond's conversion factors this means Bond A might be deliverable at 100 * 1.01 = 101.0 for a futures price of 100, and Bond B might be deliverable at 100 * 0.99 = 99.0 for a futures price of 100. Bond B has a lower coupon (and lower price) relative to Bond A so this is a good standardisation. This is how UK government bond conversion factors are derived (except I believe the nominal coupon has been lowered to 3% to bring it more inline with market rates)
Now someone at CME goes, rather than use the YTM formula with its slight difficulties in handling fractional periods, lets just write out a standardised formula which gets very close to that. After all, it doesn't matter exactly what the conversion factors are (since the nominal coupon % is arbitrarily chosen anyway), just that there are some.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.