Forward Rates Using Interest Rates
A forward exchange rate locks in today the rate for swapping currencies at a future date. Interest rate parity says that rate must offset the interest-rate gap between the two countries, or traders could earn risk-free profits. The currency with the higher interest rate trades at a forward discount.
What you will learn
- What a forward exchange rate is and why companies use it to hedge
- The covered interest rate parity formula
- How to keep the quote direction straight so you don't flip the answer
- Forward premium vs forward discount
- Why breaking parity creates a risk-free arbitrage
The formulas
- S
- spot rate, in units of currency A per 1 unit of currency B
- F
- one-year forward rate, same quote
- r_A
- one-year interest rate in currency A
- r_B
- one-year interest rate in currency B
- Positive
- currency B trades at a forward premium
- Negative
- currency B trades at a forward discount
Worked example
The spot rate is $1.25 per £1. The one-year interest rate is 4% in the US and 5% in the UK. Find the one-year forward rate.
- Quote is dollars per pound, so currency A = dollar and currency B = pound.
- F = 1.25 × (1.04 ÷ 1.05) = $1.2381 per £.
- Forward discount on the pound = (1.2381 − 1.25) ÷ 1.25 ≈ −0.95%.
- Check: $1,000 at 4% grows to $1,040. Or convert to £800, earn 5% to get £840, and sell forward at 1.2381: £840 × 1.2381 ≈ $1,040.
Answer: The one-year forward rate is about $1.2381 per pound. The pound trades at a forward discount because UK interest rates are higher, and both routes end with the same $1,040.
Common questions
How do you calculate a forward exchange rate?
Multiply the spot rate by one plus the interest rate of the quote (price) currency, then divide by one plus the interest rate of the base currency: F = S × (1 + r_A) ÷ (1 + r_B), with S in units of A per unit of B. Use rates for the same period as the forward contract.
What is covered interest rate parity?
Covered interest rate parity says that investing at home, or converting to a foreign currency, investing there, and locking in the conversion back with a forward contract, must give the same return. If not, traders could earn risk-free arbitrage profits, which pushes the forward rate back into line.
What is a forward premium or forward discount?
A currency trades at a forward premium when its forward rate buys more of the other currency than the spot rate does, and at a forward discount when it buys less. Under interest rate parity, the currency with the higher interest rate trades at a forward discount.
What is the difference between covered and uncovered interest rate parity?
Covered parity uses a forward contract to lock in the future exchange rate, so it is an arbitrage relationship that holds closely in practice. Uncovered parity replaces the forward rate with the expected future spot rate, so it is only a forecast and often fails in the short run.