How Treasury Bond Conversion Factors Change Across Delivery Months

Summary

The document raises a question about why Treasury bond futures conversion factors move in opposite directions across delivery months for bonds with coupons above or below the contract’s 6% standard. It challenges the idea that the factor’s direction should depend on current market yields, using a below-standard-coupon bond trading at a premium as an example.

The discussion highlights a key distinction: conversion factors are based on a standardized yield convention and the bond’s remaining maturity, rather than being recalculated from prevailing yields. The document itself does not provide the answer or supporting derivation, so it is best read as a conceptual question rather than a complete explanation. Its example also shows why the relationship between coupon, conversion factor, and actual market price can be confusing when market rates differ from the standard yield assumption.

Key ideas

• Conversion factors are specific to a bond and a futures delivery month.
• The question concerns why factors rise or fall with successive delivery months depending on whether the coupon is below or above 6%.
• The author asks whether this direction should depend on prevailing yields instead of the standard yield convention.
• A bond can trade at a premium while having a conversion factor below one, which motivates the question.

Tags

# Intuition behind conversion factors increasing/decreasing for longer dated expiries?


# Intuition behind conversion factors increasing/decreasing for longer dated expiries?












I'm trying to intuitively reason why the below claim from The Treasury Bond Basis is true.

> Conversion factors are unique to each bond and to each delivery month. Note in Exhibit 1.3 that conversion factors for bonds with coupons higher than 6% become smaller for each successive contract month to reflect the drift toward par of its price as it approaches maturity. Similarly, the conversion factors of bonds with coupons less than 6% drift upward for successive contract months.

It feels to me like this would be a function of the prevailing yields, not a fixed 6%. Take a 5% coupon bond for example in a 4% rate environment—in this case, conversion factor < 1 but the bond will be trading at a premium and will decay towards par, so I would think the CF would also decrease as well to account for this and keep futures price constant as time to expiry increases. But it seems I'm missing something as the switch from increasing to decreasing happens at the CF = 1 boundary as stated in the text. Is it just making the assumption that if the CF < 1 i.e. the yield is < 6% on the bond then it will be trading at a discount and increasing in price towards par? That feels like a strange assumption though given the rates have historically been so low.

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