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.
Interest rate parity explained simply
Covered interest rate parity says the forward rate must offset the interest-rate gap between two countries: F = S × (1 + r_A) ÷ (1 + r_B). Otherwise traders could make risk-free profits. In the example, $1.25 per £1 with US rates at 4% and UK rates at 5% gives a one-year forward rate of about $1.2381.
What this interest rate parity lesson covers
- 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
Interest rate parity formulas, explained
- 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
How to calculate a forward exchange rate step by step (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.
Covered vs uncovered interest rate parity
| Covered | Uncovered | |
|---|---|---|
| Uses | The forward rate (locked in) | The expected future spot rate |
| Risk | None, the rate is locked | Exchange-rate risk |
| How well it holds | Very closely in normal markets | Often fails in the short run |
Harder interest rate parity questions
What if the forward rate were $1.25 instead of $1.2381?
Borrow $1,000 at 4%, convert to £800, earn 5% to get £840, and sell forward at $1.25 for $1,050. Repay $1,040 and keep $10 with no risk. Trades like this push the forward rate back to parity.
Why does the higher-rate currency trade at a forward discount?
Holding pounds earns more interest, so the forward rate has to give back that advantage. Otherwise everyone would hold pounds and lock in the rate.
Common interest rate parity 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.