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How Interest Rate Differentials Set the Cost of Currency Hedging

Article Quant Q&A · Author: elypticla
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Summary

The document explains why a currency hedge can have an apparent annual cost even when a forward contract produces no profit or loss if the exchange rate at maturity matches the agreed forward rate. The key point is that the forward rate already reflects the interest rate difference between the two currencies and the cross-currency basis. In the example discussed, these components imply that the three-month forward rate is discounted relative to spot by roughly one quarter of the stated annualized hedge cost.

The explanation resolves the apparent contradiction by distinguishing the forward’s payoff relative to its contracted rate from the cost embedded in that rate relative to spot. It gives no independent derivation or broader market evidence, and its numerical illustration depends on the quoted rates and basis in the source passage. It is a concise conceptual explanation rather than a full treatment of hedge accounting, changing exposures, or differences among forward conventions.

Key ideas

  • A forward contract's payoff is measured against its agreed forward rate, while its implied cost is understood relative to spot.
  • The FX forward rate incorporates interest rate differentials between the currencies.
  • Cross-currency basis can also affect the forward rate and the cost of hedging.
  • A forward rate discount can reflect an annualized hedge cost over the contract tenor.

Tags

ForexFixed incomeCarryDerivatives pricing
Full text
# Why does it cost to hedge?


# Why does it cost to hedge?












In e.g. https://www.nb.com/en/ae/insights/the-opportunity-in-usd-hedged-global-treasuries it says

> A EUR-based investor who purchases a U.S. Treasury, for example, will currently give up around 310 basis points annually to insulate themselves from currency movements: this consists of the 260-basis point short rate (3-month USD LIBOR) paid away for selling the USD, the negative 35-basis point short rate (3-month EUR LIBOR) “received” for buying the EUR, plus 13 cross-currency basis points paid to swap EUR for USD. On the other hand, a USD-based investor who purchases EUR assets will “earn” this additional 310 basis points.

I'm not sure I fully understand this. I can hedge USD by simply entering into a FX Forward agreement for let's say 3 months.

After 3 months, I pay USD and receive EUR. My "profit" depends on the spot rate in 3M versus the forward rate I agreed to. So I either make money or lose money. If the spot equals the forward, then I break even.

So where exactly am I "losing" 310 basis points?

## Answer by dm63 (score 2)

https://quant.stackexchange.com/a/81024

The calculation given in the text is telling you that the 3 month forward FX rate is a discount to the spot rate by an amount equal to (3.1%/4). That is, 3.1% annual rate accrued for 3 months.

The calculation of forward fx rate depends on the interest rate differential and the currency basis, as noted. Perhaps you were thinking that the forward fx rate is a separate phenomenon, but it isn’t.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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