Distinguishing Swap Mark-to-Market Gains from Expected PnL

Summary

The document poses a fixed-income valuation question about a pay-fixed interest rate swap held for a year. It asks how a positive mark-to-market on the remaining swap, calculated as the difference between the original forward rate and the prevailing shorter-tenor swap rate, can coexist with an expected total PnL of zero when the position is unwound.

The apparent tension is framed in terms of carry and roll: the original trade is described as having negative carry, while the later unwind produces an offsetting mark-to-market gain if forward rates are realized. The text itself does not include an answer or derive the accounting, so it does not establish a general valuation method or provide empirical evidence. Its useful focus is the distinction between the value of a residual swap at a future date and the expected profit over the full holding period. Resolving the question requires specifying the valuation and cash-flow conventions and separating accrued carry from changes in the market value of the remaining contract.

Key ideas

• A residual swap can have positive mark-to-market value at the unwind date.
• The document contrasts that value with the expected PnL over the full holding period.
• It frames negative carry and a later mark-to-market gain as potentially offsetting components.
• The text asks the question but does not provide a derivation or resolution.

Tags

# What PnL is realized if swap forwards are realized?


# What PnL is realized if swap forwards are realized?












I was reading this question: MtM of interest rate swap if forward rates are realised

I'm confused by the first part of the answer, where user35980 says "So, if forward rates are realized, after one year you will be paying 𝑌 on a 4y spot swap while the market is 𝑋, so your MtM on the residual swap will be 𝑋−𝑌>0." So the MtM is positive, so you make money.

However, later on, user says that "if you enter a pay fixed 5y swap today, hold the trade for a year, and then unwind it at market, how much money do you expect to make? The answer is 0. Because the expected value of 𝑈 , 𝐸(𝑈)=𝑋 : when you enter the swap, you lock in negative carry of 𝑌−𝑋<0 . When you unwind it at the prevailing 4y rate of 𝑋 you make 𝑋−𝑌>0".

So the first time, he says that you have a PnL of X-Y, given that the forwards are realized. However, the second paragraph he says that you have a PnL of 0, because the carry and roll cancels out.

What am I missing?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.