A longer-dated FRA is a type of forward rate agreement (FRA) that has a longer time period between the settlement date and the maturity date. An FRA is a contract between two parties to exchange interest payments on a notional amount at a future date, based on a fixed rate and a reference rate, such as LIBOR. The notional amount is not exchanged, only the difference between the interest payments is settled in cash.
A longer-dated FRA can be used to hedge against interest rate risk or to speculate on future interest rate movements. For example, a borrower who expects to borrow money at a floating rate in six months can enter into a longer-dated FRA to lock in a fixed rate for the next six months, starting from six months later. This way, the borrower can protect themselves from rising interest rates and know their borrowing costs in advance. Alternatively, an investor who expects interest rates to fall in six months can enter into a longer-dated FRA to receive a fixed rate and pay a floating rate for the next six months, starting from six months later. This way, the investor can profit from the difference between the fixed rate and the lower floating rate.
The value of a longer-dated FRA depends on the difference between the forward rate and the reference rate at the settlement date. The forward rate is the implied rate for the contract period, based on the current spot rates for the two periods. The reference rate is the actual rate for the contract period, observed at the settlement date. The value of a longer-dated FRA can be positive or negative, depending on whether the forward rate is higher or lower than the reference rate. The value of a longer-dated FRA also depends on the convexity adjustment, which is a correction factor that accounts for the difference between the compounding frequency of the forward rate and the reference rate. The convexity adjustment is usually positive, meaning that the forward rate is higher than the reference rate, and it increases with the length of the contract period and the volatility of the reference rate. Therefore, a longer-dated FRA has a higher convexity adjustment than a shorter-dated FRA.
Basic Theory
An FRA is essentially a forward contract on interest rates. In a Longer-Dated FRA, the agreement typically covers a period exceeding one year. The contract specifies a fixed interest rate (the FRA rate) and a notional amount. The settlement occurs at the end of the agreed-upon period, and the payment is calculated based on the difference between the fixed FRA rate and the prevailing market interest rate.
Procedures in Excel
- Understand the Terms:
- Notional Amount: The principal amount on which the interest rate differential is calculated.
- FRA Rate: The fixed interest rate agreed upon.
- Contract Period: The duration of the agreement.
- Determine the Market Interest Rate:
- Obtain the prevailing market interest rate for the specific contract period.
- Calculate the Interest Differential:
- Find the difference between the FRA Rate and the Market Interest Rate.
- Calculate the Settlement Amount:
- Multiply the Interest Differential by the Notional Amount.
Scenario
Suppose Company A and Company B enter into a Longer-Dated FRA with the following terms:
- Notional Amount: $1,000,000
- FRA Rate: 5%
- Contract Period: 2 years
- Market Interest Rate (at the time of settlement): 4%
Excel Calculation
- Determine the Interest Differential:
=FRA Rate - Market Interest Rate =5% - 4% =1% - Calculate the Settlement Amount:
=Interest Differential * Notional Amount =1% * $1,000,000 =$10,000
Therefore, the settlement amount for this Longer-Dated FRA would be $10,000.
Other Approaches
- Forward Rate Agreement Formula:
Settlement Amount = Notional Amount * (FRA Rate - Market Interest Rate) * (Contract Period / 360)This formula accounts for the time factor using a 360-day year convention.
- Graphical Representation:Create a line chart in Excel to visualize the impact of changing market interest rates on the settlement amount, providing a dynamic understanding of the FRA’s sensitivity to interest rate movements.
