Understanding FX Swap Cash Flows, Carry, and Forward Rate Convergence

Summary

The document clarifies the cash-flow direction of an FX swap that sells euros for dollars at the near date and buys euros back at a higher forward exchange rate. Because EUR/USD is quoted as dollars per euro, the higher far-leg rate means paying more dollars to reacquire the euros, creating a loss on the exchange-rate cash flows. During the term, however, the position entails paying interest on euros borrowed and receiving interest on dollars held, which can produce positive carry in the example described.

For a view that euro and dollar interest rates will converge, the answer suggests comparing forward exposures at different maturities, such as selling EUR/USD at a later date and buying it back at an earlier one. Profit would depend on the forward rates converging as expected. This is a brief conceptual explanation rather than a full valuation: it omits currency basis, as well as detailed funding, discounting, and risk considerations.

Key ideas

• EUR/USD quotes the number of US dollars per euro, so the quote direction determines how to interpret each leg.
• Selling euros near and buying them back at a higher forward rate loses on the exchange-rate cash flows.
• Interest received on dollars and paid on borrowed euros can contribute positive carry.
• A view on rate convergence can be expressed through offsetting forward positions at different maturities.
• The explanation omits currency basis and detailed valuation considerations.

Tags

# FX Swap P&L question


# FX Swap P&L question












I am currently trying to compute the P&L of a FX swap and to understand it's implications.

Let's say when we sell 1M EUR spot eur/usd at 1.08 and at the same time buy a one month month forward eur/usd at 1.10. Then the net cash flow would be + USD $ 16,835. I have a few questions on this.

1.) Is this a P&L gain ?

2.) If it is, is the gain due to the interest carry of swap points as USD has a higher interest rate than EUR ?

3.) If I want to enter a speculation fx swap trade that the EUR interest rate will increase in one month versus the USD interest rate, then should I enter a fx swap to buy eur/usd at the near leg and sell EUR/USD opposite at the far leg ?

Thank you for your help and appreciate your explanation.

## Answer by dm63 (score 1)

https://quant.stackexchange.com/a/53055

1) no, EURUSD is quoted as USD per Euro. Therefore if you sell 1M Euros for 1.08 and buy them back one month forward for 1.10 you will lose USD 20,000.

2) during the month you will have to pay interest on the Euros you borrowed and receive interest on the dollars you own , which will be a net positive.

3) it sounds like you want to sell EURUSD 2mo forward versus buying it 1M forward. Say the 2mo rate is 1.12 and the 1Mo is 1.10. Then if the interest rates converge , these two rates would converge , delivering you a profit.

I’ve ignored the complication of the currency basis for the sake of clarity.

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