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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?

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    $\begingroup$ What is your swap? IBOR based? what is the frequency say semi-semi against 6m-IBOR? $\endgroup$
    – Attack68 ♦
    Commented Aug 30, 2023 at 12:05
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    $\begingroup$ Also what do you mean by carry? Do you actually mean roll-down? $\endgroup$
    – Attack68 ♦
    Commented Aug 30, 2023 at 12:06
  • $\begingroup$ see also: quant.stackexchange.com/questions/35795/… $\endgroup$
    – Attack68 ♦
    Commented Aug 30, 2023 at 12:08
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    $\begingroup$ carry = interest less cost of financing, independent from market moves. Also i would like to understand the general concept for a plain fixed vs flat swap independently from the specifics $\endgroup$
    – Finance_student
    Commented Aug 30, 2023 at 12:50
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    $\begingroup$ IRSs, which are derivatives are not like securities. They do not pay interest and they do not require financing, therefore the intrinsic cost of carry is zero. If the market evolved as initially priced your IRS contract would be worth precisely zero by the end of its life. (this assumes the contract is collateralised and remunerated at the same rate as which its cashflows are discounted, which is standard for cleared IRS) $\endgroup$
    – Attack68 ♦
    Commented Aug 30, 2023 at 17:08

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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

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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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  • $\begingroup$ you mean 6-month carry=(Fixed Rate−Float Leg Fixing)* Dv01 = bps * PnL per bp = (4%-2%) * 0.03% in my example? DV01 is not divided but multiplied? $\endgroup$
    – Finance_student
    Commented Oct 17, 2023 at 23:00

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