Converting Swap Carry from Upfront Value to Running Basis Points
Summary
The document addresses a practical interest rate swap carry calculation and clarifies the role of a six-month discount factor. It describes calculating upfront carry as the difference between the five-year swap rate and six-month Euribor, multiplied by the discount factor and the half-year accrual period. The resulting upfront amount is then divided by the DV01 of the forward-starting swap to express carry in running basis points.
The example reports an upfront carry of 35 basis points and a running carry of 7.9 basis points, matching the difference between the forward-starting swap rate and the spot five-year rate. Another answer notes that an implicit factor of about two can arise from the six-month coverage convention. The discussion indicates that the original note’s notation may be incomplete or imprecise; the calculation depends on the stated instrument conventions, discount factor, and DV01, so it should not be treated as a universal formula without checking those definitions.
Key ideas
- The discount factor P(0,6M) represents discounting to the six-month date in the example.
- Upfront carry uses the swap rate minus the six-month floating rate, scaled by the discount factor and accrual period.
- Convert upfront carry to running basis points by dividing by the relevant forward swap DV01.
- The example's running carry agrees with the difference between the forward-starting and spot swap rates.
- Ambiguous notation and an implicit half-year factor can make the source formula difficult to reproduce.
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Full text
# Carry Roll Calculation for Interest Rate Swaps in Nordea Note # Carry Roll Calculation for Interest Rate Swaps in Nordea Note In the Nordea note linked in few other posts related to carry roll calculation there is a calculation/example for the formulas provided. https://corporate.nordea.com/api/research/attachment/2796 I'm struggling to replicate the carry calculation in the research note with the practical example. 5Y swap is 1.023% , 6M euribor = 0.319%. DV01 for 4.5Y swap in 6 months time is 4.45. Author also defines P(0,6M)=0.995 Then the carry calculation using formula 1a in the note is 0.995 . (1.023%-0.319%) / 4.45 = 7.9bps Author doesn't explain what P(0,6M) is and it's not defined in the original formula for the carry calculation. First of all what is this p(0,6M)? It doesn't change the calculation much as it is quite close to 1 but curious as to what it is. And eventually above formula doesn't really result in 7.9bps but it is actually close 16bps. Not sure if he then divides it by 2. While the carry from other formula: (4.5Y swap in 6 months time - 5Y spot swap) is indeed 7.9bps. Could someone please explain what P(0,6M) is and how the carry calculation from 1a results in 7.9bps? Thanks ## Answer by user68819 (score 1, accepted) https://quant.stackexchange.com/a/79765 Think there's some typos and sloppy notation. Carry for the 5y swap in bps upfront: (5y swap - 6m euribor) × dv01(6m) Where dv01(6m)=0.5 × df(6m) So using the example bps carry up front: (1.023% - 0.319%) × 0.5 × 0.995 = 35bps It is fairly easy to then see to convert this to bps running of 6m4.5y swap you'd divide through by its dv01, giving you a carry of: (6m 4.5y swap - 5y swap) And again continuing the example : 35bps/4.45 = 7.9bps = (6m 4.5y - 5y) = 1.10% - 1.023% ## Answer by Big L (score 0) https://quant.stackexchange.com/a/85403 It is divided by roughly 2 (the specific coverage for 6 months will average 2). It's a bit sloppy that that is implicit and doesn't appear explicitly.
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