Interpreting Bond Carry and Roll in Running and Upfront Basis Points
Summary
The document distinguishes running basis points from upfront basis points in bond risk and carry calculations. Upfront basis points translate a running spread into a price-risk amount using DV01, the dollar value of a one-basis-point yield move; the conversion therefore depends on the bond’s sensitivity. A quoted yield spread by itself is neither a running nor an upfront carry measure.
Carry and rolldown are generally reported in running basis points over a specified holding horizon. Expected profit and loss over that horizon is estimated by multiplying the running amount by PV01, and the figures should not be assumed to be annualized. For a spread position, the answer recommends calculating carry and rolldown for each bond, then comparing them after sizing the legs to equal DV01. It illustrates the conversion and a duration-neutral two-bond trade with stated examples. These are horizon-specific estimates, and the explanation does not address realized returns or changes in the yield curve.
Key ideas
- Upfront basis points convert running basis points using DV01, so the conversion varies with bond risk.
- Running carry and rolldown figures describe expected profit and loss over a stated horizon and are not necessarily annualized.
- A simple yield spread does not directly measure carry or rolldown.
- For a bond spread trade, calculate each leg’s carry and rolldown and compare them after matching DV01.
- PV01 translates running basis point estimates into expected monetary profit and loss for a position.
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Full text
# Carry and roll (upfront vs running)
# Carry and roll (upfront vs running)
I am still confused regarding the differences between upfront and running. If two bonds have a spread of 50bp, does that equate to 50bp in total return over the course of the year or do I have to multiply 50bp by the duration effect.
Sometimes I mix up the two and don't know which space I'm in.
## Answer by Helin (score 3, accepted)
https://quant.stackexchange.com/a/35788
Bps running and bps upfront are used so that notional amount doesn't need to be referenced, and "bps upfront" is just "bps running" multiplied by DV01 (not modified duration).
For example, a 10-year bond currently has a DV01 of roughly 9. Then "1 bp running" for this bond is equivalent to "9 bp upfront". If the notional amount is \$100 million, then the total dollar risk is $9 \text{ bps} \times \text{100 million} = \$90,000$.
Carry and roll for bonds/swaps are usually quoted in "bps running" terms over a specified horizon. If a bond's RD&C (rolldown + carry) is $x$ bps running over 3 months, it means that your expected P&L from carry and roll will be $x \text{ bp} \times \text{PV01}$ over three months. Continuing with our 10-year bond example, its RD&C is currently about 4.4 bps running, or 39.6 bps upfront, or \$396,000 for 100 million notional. Note that we don't usually annualize carry and roll statistics when we report them, so these are expected P&L over the specified horizon (3 months in this case).
Also note that bps running is bond specific, "1 bp running" would equate to "$x$ bp upfront" depending on a bond's risk. So the simple yield spread between two bonds is neither bps running nor bps upfront. Typically we'd calculate the carry/roll for each bond and then take the difference. The result would be considered a "bps running" concept and you'd implement a spread trade in a DV01-neutral way (i.e., you'd scale the notionals on the two bonds so that their DV01s are identical).
Let's use a real life example: 10-year bond yield closed at 2.17% today while 30-year bond yield closed at 2.75%, a yield spread of 58 bp. If we implement a duration-neutral spread trade (say short 2.27 units of 10-year bond against each unit of 30-year bond), the 3-month carry of the trade would be $1.9-2.7 = -0.8$ bp running and the 3-month rolldown is $0.1 - 1.7 = -1.6$ bp running.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.