How Bond Futures Conversion Factors Reduce Delivery-Basket Price Gaps
Summary
The document explains the role of conversion factors in bond futures with a basket of deliverable bonds. A conversion factor adjusts each bond’s invoice price using a standardized reference yield assumption, making bonds with different coupons more comparable for delivery. Without that adjustment, lower-coupon bonds may be much cheaper to deliver than higher-coupon alternatives, which can concentrate delivery demand on a small set of issues.
That concentration can create a delivery squeeze if a market participant controls much of the cheapest-to-deliver bond’s available supply. By narrowing delivery-price differences, conversion factors can make it more feasible to switch to another eligible bond if the cheapest issue is unavailable. The explanation compares delivery prices with and without the adjustment across yield shifts, but the referenced charts are not included in the text. It also stresses that the adjustment is imperfect: bonds do not become identical in value or delivery economics, and relative attractiveness can still vary with yields.
Key ideas
- A bond futures conversion factor adjusts invoice pricing to make eligible bonds more comparable for delivery.
- Without conversion factors, coupon differences can make one bond consistently cheaper to deliver.
- Concentrated demand for a cheapest-to-deliver bond can expose the market to a delivery squeeze.
- Conversion factors reduce, but do not eliminate, delivery-price differences across the basket.
- Relative delivery economics can still change as yields move.
Tags
Full text
# When a particular bond is delivered, why there is the need to define a conversion factor? What is its utility?
# When a particular bond is delivered, why there is the need to define a conversion factor? What is its utility?
Where, the conversion factor for a bond (by John C. Hull) is set equal to the quoted price the bond would have per dollar of principal on the first day of the delivery month on the assumption that the interest rate for all maturities equals 6% per annum (with semiannual compounding)
## Answer by Helin (score 2, accepted)
https://quant.stackexchange.com/a/33202
The purpose of conversion factor is to make bonds in the delivery basket more equally deliverable (theoretically anyways, but the process is not perfect).
This is an important design decision for bond futures. Without conversion factor, bonds with low coupon rates will have significantly lower prices than their high coupon peers in the delivery basket, making them de facto cheapest-to-deliver (CTD) issues. A smart investor can buy up all available supply of these low coupon bonds, making it impossible for other market participants to make delivery ("delivery squeeze").
With conversion factors, the bonds become much more similar from a delivery price perspective. If the CTD is cornered by one investor and not obtainable, we simply move to the next possible CTD without incurring too significant a penalty.
In this chart below, I'm drawing the delivery prices of three bonds under various parallel yield shifts, WITHOUT the conversion factor adjustment:
Clearly the 4% coupon issue is dominantly cheap. If that issue is not available, I'd have to deliver the next cheapest bond (the 6% issue), whose price is much much higher.
The next chart shows delivery prices for the same three bonds WITH conversion factor adjustments:
As said, the process is not perfect, but the differences are now much more tolerable.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.