Swap Carry, Forward Rates, and the Difference Between PnL and MtM

# How does carry create a “buffer” in swap MtM?


# How does carry create a “buffer” in swap MtM?












Background:

I interned on a fixed income sales desk at a BB, so I tend to think about swaps from a practitioner / intuition-first perspective. I’d especially appreciate an intuitive explanation rather than a purely formal one.

Setup (ignore bid/offer and transaction costs):

At ( $t_0$ ):

- 10y spot swap rate: 4%

- 5y spot swap rate: 2%

- 5y5y forward swap rate: 6% (Using a simple no-arbitrage approximation: $ (1+4\%)^{10} = (1+2\%)^5 (1+f)^5 $

At ( $t_5$ ):

- 5y spot swap rate: 5%

From e.g. the Nordea note, carry is often approximated as:

- 5y carry ≈ (6% - 4% = 2%)

The confusion:

At ( $t_0$ ), I enter a 10y receiver swap at 4%.

At ( $t_5$ ), I now hold a 5y receiver, while the market rate is 5%. Intuitively, I am receiving 1% below market, so I would expect a negative MtM.

However, on the desk people often said that “you have to beat the forward”, i.e. MtM only turns negative if the rate rises above 6% (the forward), not just above 4%. I’ve also seen statements that the swap can still have positive MtM despite rates rising.

This seems inconsistent with the usual replication argument:

- If I enter a 5y payer swap at 5% in ( $t_5$ ), floating legs cancel

- I’m left paying 5% vs receiving 4% → clearly negative value

Carry intuition / “buffer” argument:

What I heard on the floor:

- Receiver swaps have a carry buffer in a rising rate environment

- Payer swaps face a carry barrier

Trying to reconcile this, I considered the following replication:

- At ( $t_0$ ), enter a 10y receiver at 4%

- Also enter a 5y5y forward payer at 6% (to unwind in 5y)

- This locks in future unwind conditions

At ( $t_5$ ):

- The forward payer (6%) offsets the remaining 5y of the receiver (4%)



Now consider the reverse trade (10y payer + 5y5y receiver):

- This seems to produce +2% net receiving → apparent arbitrage

So the only way this is consistent is if:

- The initial 10y receiver already has enough positive value (“carry buffer”) to offset the future −2%

- And symmetrically, a 10y payer has negative carry that offsets the +2%

Question:

Is this the correct way to think about swap carry?

More specifically:

- Why does MtM only turn negative once the spot rate exceeds the forward (6%), rather than the original fixed rate (4%)?

- Where exactly does the “carry buffer” show up in the valuation to eliminate the apparent arbitrage?

## Answer by shreyase99 (score 0)

https://quant.stackexchange.com/a/85653

Based on your description, the problem seems to be in the definition of MtM.

Let's assume that the market behaved the same way between times $t_{0}$ and $t_{5}$, as it was projected at time $t_{0}$. To make things way simpler, I could say that the floating rates stayed at 2% throughout these first 5 years and thus, the swap rate of the swap ending at $t_{5}$ ($swap_{5y}$).

This means that when you look back from $t_{5}$ you would see that your receiver $swap_{10y}$ locked-in at 4% has been returning better than $swap_{5y}$ all along. The cumulative excess returns from this phase is your 'carry buffer'.

Over the next 5 years, even if the rates for the swap starting at spot and ending at $t_{10}$ are quoted as 6% everyday, the $swap_{10y}$ paying 4% won't end up in loss at $t_{10}$ as it had already made up for the 'losses' of this phase during the first 5 years. The 4% quoted for it at $t_{0}$ had priced this in. However, if the $t_{10}$ swap rates remain above 6%, then the carry of your $swap_{10y}$ falls to zero before $t_{10}$ and falls further, giving net-loss over its lifetime. Please note that I am also making the approximations that you have made. I am also assuming that the quotes for such non-standard expiries are available.

At $t_{5}$, carry/carry buffer is a backward looking measurement. In strict terms, it has nothing to do with the MtM, which is supposed to be the discounted value of the forward-dated cashflows.

$PnL = Carry + MtM$

Taking another scenario, if the rates between $t_{0}$ and $t_{5}$ had remained above 2% throughout, then you would be left with a thinner carry buffer for $t_{5}$ to $t_{10}$. In this case, at $t_{5}$, $PnL$ can become negative even at $swap_{10y}$ spot rates of <6%.

I hope this clarifies your doubt.