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Estimating a One-Year USD/CHF Rate from Interest-Rate Differentials

Article Quant Q&A · Author: Darren Seah
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Summary

The document illustrates how to estimate a future USD/CHF exchange rate from the current spot rate and the two currencies’ one-year interest rates. It grows one unit of each currency at its respective rate, then compares the resulting amounts to infer the exchange rate consistent with those values. With the stated inputs, the calculation gives an implied rate of 1.67875 CHF per USD in one year.

This is a compact illustration of covered interest parity intuition: currencies with different interest rates have an implied forward relationship to prevent a risk-free arbitrage under the relevant assumptions. The example does not discuss forward contracts, transaction costs, compounding conventions, or the distinction between a market forward rate and an expectation of the future spot rate. Its wording treats the calculation as an expected future spot, which need not match the realized exchange rate.

Key ideas

  • Grow each currency at its own one-year interest rate before comparing values.
  • The example derives an implied USD/CHF rate by dividing the future CHF value by the future USD value.
  • Interest-rate parity gives a pricing relationship, not a reliable forecast of the realized future spot rate.
  • Market frictions and conventions are not addressed in the calculation.

Tags

ForexCarryArbitrage
Full text
# How to calculate Spot Rate with interest rate


# How to calculate Spot Rate with interest rate












You are a foreign exchange trader specialized in the US dollar Swiss franc market (USD/CHF). One morning, you notice that the one-year dollar interest rate is 4%, while the one-year interest rate on Swiss francs is 2.7%. Today’s USD/CHF rate is $1.7. What spot rate do you expect for the USD/CHF in one year?

## Answer by andrewleef1 (score 4)

https://quant.stackexchange.com/a/45359

1 USD today will be worth 1.04 USD in 1 year. Similarly, 1.7 CHF today will be worth 1.7459 CHF in 1 year. As a result, we can expect the USD/CHF rate in one year to simply be 1.7459/1.04 = 1.67875.

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.