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Absolute and DV01-Relative Carry for Interest Rate Swaps

Article Quant Q&A · Author: junior_pm
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Summary

The document asks why six-month carry on a fixed-floating interest rate swap is divided by DV01 in a cited market-research calculation. The questioner expects carry to be the difference between the fixed and floating legs and is unsure why a risk sensitivity appears as a divisor.

The response distinguishes absolute carry, measured as a cash or notional amount earned over the holding period, from relative carry, expressed as an equivalent change in the swap rate. DV01 converts between these representations: a given amount of notional carry can be divided by the swap's DV01 to express it in rate-equivalent terms. The example illustrates the distinction using carry and DV01 values. This is a unit-conversion explanation; it does not provide a general pricing derivation, and the exact scaling depends on the instrument and the convention used for DV01.

Key ideas

  • Carry can be quoted as an absolute amount or as a rate-equivalent measure.
  • DV01 relates a swap's value change to a change in its rate.
  • Dividing absolute carry by DV01 expresses the carry in rate-equivalent units.
  • The interpretation depends on consistent units and the instrument's DV01 convention.

Tags

Fixed incomeCarryRisk management
Full text
# Why is carry divided by DV01 to scale it?


# Why is carry divided by DV01 to scale it?












If I understand correctly, 6M carry in a fixed-floating interest rate swap should be the difference between the fixed and floating leg.

When I read this on Page 2: https://corporate.nordea.com/api/research/attachment/2796

The 6M carry is DIVIDED by DV01. Why is this? I can see why you would multiply by the DV01 to get the absolute value, but why scale it?

E.g. $Carry(6M) = \frac{SR(0,5Y)-F(0,6M)}{dv01(Swap(6m,4.5Y))}$ whereby $SR(0,5Y)$ is the 5Y spot swap rate at inception and $F(0,6M)$ is the 6M floating fixing.

## Answer by Chris Edmonton (score 1)

https://quant.stackexchange.com/a/71650

Page 1 says that "carry & roll can be given in relative or absolute terms". For example, if, over a holding period, you earn 10bp of notional on a swap that has a DV01 of 4.5, what you earn has the same value as a 2.2bp change in the swap rate, so: absolute carry = 10bp (of notional), and relative carry = 2.2bp (of swap rate) (i.e., in market jargon: 2.2bp "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.