Understanding FX Forward Rate Calculation
Foreign exchange (FX) forward rates are crucial instruments in international finance, allowing businesses and investors to lock in an exchange rate for a future transaction. Unlike spot rates, which are for immediate settlement, forward rates are agreed upon today for a transaction that will occur at a specified future date. This hedging mechanism protects against unfavorable currency fluctuations.
The calculation of FX forward rates is based on the principle of Interest Rate Parity (IRP). IRP suggests that the difference in interest rates between two countries should be equal to the difference between the forward and spot exchange rates. In simpler terms, the cost of hedging currency risk through a forward contract should be equivalent to the cost of borrowing in one currency, converting it to another, investing it, and then converting it back at the spot rate.
The Formula
The most common formula for calculating a 1-year forward rate is:
Forward Rate = Spot Rate * ( (1 + Domestic Interest Rate) / (1 + Foreign Interest Rate) )
For tenors other than one year, the interest rates are adjusted proportionally based on the number of days in the tenor relative to a standard year (typically 360 or 365 days).
The formula adjusted for tenor (in days) is:
Forward Rate = Spot Rate * ( (1 + (Domestic Interest Rate * Tenor Days / 360)) / (1 + (Foreign Interest Rate * Tenor Days / 360)) )
Where:
- Spot Rate: The current market exchange rate for immediate delivery.
- Domestic Interest Rate: The interest rate applicable to the currency being bought (the "price" currency in the quote, e.g., USD in EUR/USD). It's usually quoted as an annual percentage.
- Foreign Interest Rate: The interest rate applicable to the currency being sold (the "base" currency in the quote, e.g., EUR in EUR/USD). It's usually quoted as an annual percentage.
- Tenor Days: The number of days until the forward contract settles. We often use 360 days for calculation in the FX market (known as Actual/360 convention).
Example Calculation
Let's consider an example for EUR/USD.
- Current Spot Rate (EUR/USD): 1.1000
- Domestic Interest Rate (USD): 2.5% per annum
- Foreign Interest Rate (EUR): 1.0% per annum
- Tenor: 90 days
Using the formula with a 360-day year convention:
Forward Rate = 1.1000 * ( (1 + (0.025 * 90 / 360)) / (1 + (0.010 * 90 / 360)) )
Forward Rate = 1.1000 * ( (1 + 0.00625) / (1 + 0.0025) )
Forward Rate = 1.1000 * (1.00625 / 1.0025)
Forward Rate = 1.1000 * 1.0037406...
Forward Rate ≈ 1.1041
Therefore, the 90-day forward rate for EUR/USD would be approximately 1.1041. This means you can agree today to exchange EUR for USD at this rate in 90 days, effectively hedging against any potential rise in the USD relative to the EUR during that period.