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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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).

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?

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.

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.

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