Comparing Yield-Based and Price-Based Sovereign Bond Carry

Summary

The document compares two ways to describe carry on a sovereign bond: the difference between its yield and repo financing rate, and the difference between a forward bond yield and its current yield. A five-year, par bond example produces different figures under the two calculations, prompting the question of whether they should agree.

The responses explain that these measures use different units. Forward-yield carry is expressed as yield on the shorter-maturity bond at the forward date, while the repo-based figure is an upfront price or financing amount; translating the yield difference into price terms requires considering duration. Another response characterizes carry as option-adjusted spread plus rolldown and notes that yield comparisons alone omit the term-structure slope. The brief exchange gives intuition rather than a full derivation, and its approximate duration conversion is not a general exact equivalence.

Key ideas

• Repo-based carry and forward-yield carry can be expressed in different units.
• A yield difference on a shorter-maturity bond must be translated into price terms for comparison.
• Duration provides an approximate link between a yield change and an upfront price change.
• The slope of the term structure contributes to rolldown and can affect carry analysis.

Tags

# carry for a sovereign bond


# carry for a sovereign bond












For sovereign bond, I saw two carry calculations: one would be forward yield - spot yield, the other would be spot yield - repo rate. I would assume these 2 methods result in same or very close result. But that is not the case. Did I misunderstand something here?

For example, a 5 year bond with 5% coupon and 5% yield, current price = 100, say 4% repo rate, then the carry would be 5% - 4% = 1% based on the yield minus repo rate method. The 1 year forward price would be 99 (=100-(5-4)), and with the 5% coupon and 4 years to maturity, the 1 year forward yield would be 5.284%, then carry would be 5.284% - 5% = 0.284% (based on forward yield minus spot yield method). 1% versus 0.284%, this is quite different, right?

## Answer by dm63 (score 3)

https://quant.stackexchange.com/a/47449

Ah, but the 0.284% ‘carry’ is expressed in units of yield on a 4yr bond. The value of this in upfront terms is approximately 4*0.284% which is in the same ballpark as the 1% number.

## Answer by Vitomir (score 0)

https://quant.stackexchange.com/a/47410

carry = OAS + rolldown. If you look just at the yields you miss considering the slope of the term structure

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