Returns of an interest rate swap

I would like to calculate returns for a plain-vanilla (fixed-for-floating) interest rate swap. Consider, that I am long in USD 5-year swap rate, i.e. I'm holding a receiver swap for 5-year swap rate with notional of 100 $. At initiation, the swap should be valued at 0 $, as both the fixed leg and the floating leg of the swap should have the same value.

If I valuate the receiver swap a month later and it would have a value of let's say 2$, then how should I calculate the return? Is it just (2$ - 0$) / 100 $, i.e. change of price relative to the notional? I can't quite figure out how I could calculate the return by comparing change of price to previous price, as it can be at initiation 0$. On the other hand, why should I calculate the return relative to notional? After all, I am not investing any capital on the swap.

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Comments (5)

May 7, 2022 - 12:15am
CharlieBuckeroo, what's your opinion? Comment below:

From buyer's perspective, the MTM is (floating rate + spread) * notional - fixed fee rate * notional. The performance of the swap is calculated as MTM / notional, i.e. 2/100 in your example. If your goal is to compute the return on the capital (cash) you put in (return on investment?), you could instead compute 2/(initial margin + variation margin).

May 7, 2022 - 6:50am
miro.lammi, what's your opinion? Comment below:

Thanks for your reply! Why do I measure the performance relative to notional, though? As you state, it is different from measuring return on the capital. What is the purpose of measuring performance relative to notional?

May 7, 2022 - 3:52pm
CharlieBuckeroo, what's your opinion? Comment below:

I suppose it's for the same reason why % returns of stock investments are calculated relative to notional (price paid * # of shares) instead of to whatever margin your broker requires for that position. Margin requirements change over time. Calculating MTM over initial notional provides a consistent way to measure performance.

May 9, 2022 - 10:50am
Scapinetto, what's your opinion? Comment below:

Hi Miro,

You should look into the DV01 of your IRS then check the carry + rolldown + diff in fixed rate @ MtM valuation time vs. Original fixed rate paid/received.

There is no point in looking at the notional of an IRS as it does not make sense when thinking in returns.

Traders will think "i'm putting a 100k bp01 paid position in 10y $ swap" So if rates go up by 1bp,they make 100k $ - they will not compute their PnL return out of the swap notional.

"Never doubt that a small group of thoughtful, committed citizens can change the world; indeed, it's the only thing that ever has" - Margaret Mead
May 9, 2022 - 11:53am
AKvB, what's your opinion? Comment below:

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