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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

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    $\begingroup$ P(0,6m) is likely to be the 6m discount factor. I don't know what this calculation is doing because personally I make the statement that: IRS do not have carry: if the curve evolves exactly as predicted a Swap will not gain or lose PnL, however it may well be split between received/paid cashflows (Cash Asset/Liability) and remaining cashflows (NPV of Derivative Liability/Asset). Roll down is a separate calculation and assumes that the market moves in a very specific way (that is that the present yield curve is maintained). $\endgroup$
    – Attack68 ♦
    Commented Jun 17 at 5:17

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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%

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  • $\begingroup$ thanks. I struggle to conceptualise carry using dv01. formula in the note for carry is also (5y swap - 6m euribor) / dv01(swp(6m,4.5Y)) . however it goes on to say that both formulas can be multiplied by dv01(swp(6m,4.5Y)) to calculate upfront carry. upfront would be then just be (5y swap - 6m euribor) different than your formula,that is if the note is correct but as mentioned it's quite sloppy, your carry formula above Dv01 is for 6m or should it also be dv01(6m,4.5Y)? and also why is dv01(6m)=0.5 × df(6m).would it be possible to give an example with the numbers in the note? $\endgroup$
    – nichel
    Commented Jun 17 at 13:37
  • $\begingroup$ Edited my answer. $\endgroup$
    – user68819
    Commented Jun 17 at 15:42
  • $\begingroup$ thanks this is much more clear with the example. Is it fair to say that 6m carry is dv01(6m)=0.5 × df(6m) and if we'd need to calculate 3 months carry would it be dv01(3m)=0.25 × df(3m)? I think I just don't understand where the formula for dv01(6m) comes from and how it is used in the carry calculation? Also the formula in the note is then wrong as it doesn't really take into account dv01(6m) in the formula and indeed the calculation as per my original post is wrong. To confirm the carry formula in running bps = (5y swap - 6m euribor) × dv01(6m) / dv01(6m4.5y)?Many thanks again for your help $\endgroup$
    – nichel
    Commented Jun 17 at 21:49

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