Swap Carry and the Role of Forward Swap DV01
Summary
The document asks how to estimate six-month carry on a spot-starting interest rate swap and why the DV01 of the remaining forward-starting swap is used. It frames carry as arising from the difference between the swap’s fixed rate and the floating leg fixing, with DV01 representing sensitivity of value to a small rate move.
The answer associates the forward swap’s DV01 with the period being assessed, illustrated by a six-month-to-four-and-a-half-year swap. It contrasts this with the spot-starting swap DV01, which covers a different maturity profile. The explanation is brief and its displayed carry expression is ambiguous about whether the rate difference is multiplied or divided by DV01; it does not clearly derive units, sign conventions, discounting, or accrued cash flows. Treat it as an introductory intuition rather than a complete swap carry calculation methodology.
Key ideas
- DV01 measures how a swap’s value changes for a small change in interest rates.
- Carry is connected to the difference between the fixed rate and the floating leg fixing.
- The response uses the forward-starting swap’s DV01 to represent the swap exposure over the period under review.
- The document does not fully specify the formula’s units, sign convention, or cash flow treatment.
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# Carry for an Interest Rate Swap # Carry for an Interest Rate Swap I don't get why for calculating the carry of a spot starting swap I need to adjust the difference between the fixed rate and fixing by the Dv01? For example if I receive in a 5y swap and want to estimate the 6m carry i should do: ``` 5y fixed rate = 4% float leg fixing = 2% Dv01 of 6m4.5y swap = 3 6m carry = (4%-2%)/3 ``` also why would I use the Dv01 of the forward starting swap and not the dv01 of my spot starting swap? ## Answer by Amit Kumar Jha (score 0) https://quant.stackexchange.com/a/77013 In calculating the carry of a spot-starting swap, you're essentially determining the "carry" or the profit or loss that arises from the difference between the fixed rate and the float leg fixing. The Dv01 (Dollar Value of a Basis Point) is used to measure the sensitivity of the swap's value to a one basis point (0.01%) change in the interest rate. In your example, the 5-year fixed rate is 4%, and the float leg fixing is 2%. The Dv01 of a 6-month to 4.5-year swap is given as 3. The formula you're using for the 6-month carry: 6-month carry=Fixed Rate−Float Leg Fixing/Dv01 This formula is calculating how much you would gain or lose for a one basis point change in the interest rate, considering the sensitivity of the swap's value (given by Dv01). In other words, it's assessing how the swap's value changes due to the difference between the fixed rate and the float leg fixing. The reason you're using the Dv01 of the forward starting swap (6-month to 4.5-year) is that you're trying to measure the impact of a change in interest rates over the period in question (6 months to 4.5 years). The Dv01 of the spot-starting swap would not capture this specific time period and would not be appropriate for measuring the carry over the chosen period. By using the Dv01 of the forward starting swap, you're aligning your calculation with the actual time frame (6 months to 4.5 years) over which you're assessing the carry.
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