A forward rate agreement (FRA) is a contract between two parties that determines the interest rate to be paid on a future date. The interest rate is fixed at the time of the contract, but the payment is made when the contract expires. The payment is based on the difference between the fixed rate and the market rate on the expiration date. The payment is also adjusted by the notional amount of the contract and the number of days in the contract period. The notional amount is not exchanged, but is only used to calculate the payment.
An example of a FRA settlement is as follows:
- Party A and Party B enter into a 3×6 FRA with a notional amount of $1 million and a fixed rate of 5%. This means that Party A agrees to pay Party B 5% interest on $1 million for a period of three months, starting in three months from now.
- On the expiration date, the market rate for a three-month loan is 6%. This means that Party B could borrow $1 million at 6% interest for three months if they did not have the FRA.
- The payment is calculated as follows:
- The difference between the fixed rate and the market rate is 1% (6% – 5%).
- The payment is 1% of $1 million, which is $10,000.
- The payment is adjusted by the number of days in the contract period, which is 90 days (assuming a 360-day year).
- The payment is $10,000 x 90 / 360, which is $2,500.
- The payment is discounted by the market rate to reflect the present value of the payment. The discount factor is 1 / (1 + 0.06 x 90 / 360), which is 0.9852.
- The payment is $2,500 x 0.9852, which is $2,463.
- Party A pays Party B $2,463 on the expiration date. This is the net amount that Party B gains from the FRA, as they effectively pay 5% interest instead of 6% interest on $1 million for three months.
Basic Theory:
- Forward Rate: The future interest rate agreed upon today for a specified future period.
- Net Interest Difference: The settlement amount is determined by the net interest difference between the forward rate and the actual market rate at the time of settlement.
Procedures:
- Agreement: Two parties agree on a future interest rate (forward rate) for a specified period.
- Calculation Period: The calculation period is typically a short-term period within the overall FRA duration, known as the settlement period.
- Market Rate Determination: At the end of the calculation period, the prevailing market rate for the same period is compared with the agreed forward rate.
- Settlement: The party owing the net interest difference makes a payment to the other party.
Excel Formulas and Scenario:
Scenario:
Let’s consider a scenario where Party A enters into a 3-month FRA with Party B to hedge against rising interest rates. The notional amount is $1,000,000, and the agreed forward rate is 5%.
Excel Table:
| Period | Forward Rate (%) | Market Rate at Settlement | Notional Amount |
|---|---|---|---|
| 1 | 5 | 5.2 | $1,000,000 |
| 2 | 5 | 5.5 | $1,000,000 |
| 3 | 5 | 5.8 | $1,000,000 |
Excel Formulas:
- Enter the periods (e.g., 1, 2, 3 for months) in column A.
- In cell B2, enter the agreed forward rate (5%).
- In cell D2, enter the notional amount ($1,000,000).
- Use a random number generator or market data for column C.
Calculation:
The net interest difference for each period is calculated as follows:
Net Interest Difference = ((Market Rate – Forward Rate) / 100) * Notional Amount * (Days in Period / 360)
Sum up the net interest differences for all periods.
Result:
Suppose the market rates at settlement are 5.2%, 5.5%, and 5.8% for months 1, 2, and 3, respectively.
Net Interest Difference = ((5.2% – 5%) / 100) * $1,000,000 * (30 / 360) + ((5.5% – 5%) / 100) * $1,000,000 * (31 / 360) + ((5.8% – 5%) / 100) * $1,000,000 * (30 / 360)
Other Approaches:
- Using Excel’s RATE Function: Excel’s RATE function can be used to calculate the implied forward rate directly.
- Visualizing with Charts: Create charts to visualize the impact of changing market rates on the settlement amount.
