How Interest Rate Differences Create Spot Risk in FX Swaps
Summary
The note explains why an FX swap can retain a small exposure to the future spot rate even when its near and far legs exchange the same domestic notional. The key is that the notional returned at maturity does not include the interest that would have accrued on the initial cash flows. Comparing the swap cash flows with the interest that would accrue on each currency reveals a residual amount in both currencies.
In the EUR/USD illustration, the residual amounts match at the forward rate, so the example has no profit or loss if the terminal exchange rate equals that rate. A different terminal spot rate changes the value of the residual and creates the spot exposure. The explanation is intuitive rather than a full valuation treatment: the example assumes stated rates and a particular cash-flow setup, and it notes that lower interest rates make the discrepancy, and thus this component of risk, smaller.
Key ideas
- An FX swap returns the same domestic notional at maturity even though the initial cash flows would accrue interest.
- The gap between the returned notional and the interest-adjusted cash flows creates a residual currency exposure.
- The residual amounts offset at the forward rate in the illustration, but a different terminal spot rate can produce a gain or loss.
- The spot-risk component tends to be smaller when the relevant interest rates are lower.
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Full text
# What is the intuitive explanation for the spot risk in an FX swap? # What is the intuitive explanation for the spot risk in an FX swap? I am familiar with FX swap and the basis/IR risk they carry. However, know that they have a very small spot risk component which arises from the present value of future cash flows different from the value of cash flows today. Can someone please provide an intuitive explanation of where this spot risk actually arises ? ## Answer by Attack68 (score 1, accepted) https://quant.stackexchange.com/a/44569 I have only traded a few FX swaps and not in a while so do correct me if my understanding of their technical product specification is not correct: > A Purchase of an FX Swap with say, a 3M tenor, at an initially struck spot rate and forward rate demands the spot receipt of a nominal amount of domestic currency and the payment of rate equivalent foreign currency. At the end of the 3M tenor the same domestic notional amount is paid back and the foreign currency is received adjusted by the forward rate. The key to your question, I believe, is the fact that the same domestic notional is received back after 3months, when under traditional (no arbitrage) scenarios that amount would have grown by an amount equivalent to the (cross-currency adjusted) rate of interest. Suppose for EURUSD; spot: 2.0000, 3m fwd: 2.0100, FXFWD: +100 pips. Suppose EUR interest rate is 4% p/a and in USD it is 6.04% p/a. Suppose you purchase EUR1000 EURUSD FX swap at 100pips struck at 2.000 Your cashflows look like this from the FX swap: ``` Date EUR USD Today 1000 -2000 3m fwd -1000 +2010.1 ``` But don't forget about the interest over 3M: ``` Intst 10 -30.2 Total 10 -20.1 ``` If the FX rate at the end of the period is 2.01 as predicted then 10 eur == 20.1 usd so you have zero PnL, but if it deviates you have either a small loss or a small gain. It is this component that you have FX exposure to. The smaller interest rates are the smaller this discrepancy so the risk is reduced.
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