# Forward Rate Agreement (FRA): Definition, Formulas, and Example

## What Is a Forward Rate Agreement (FRA)?

A forward rate agreement (FRA) is an over-the-counter (OTC) contract between parties that determines the rate of interest to be paid on an agreed-upon date in the future. In other words, an FRA is an agreement to exchange an interest rate commitment on a notional amount.

The forward rate agreement determines the rates to be used along with the termination date and notional value. FRAs are cash-settled. The payment is based on the net difference between the interest rate of the contract and the floating rate in the market—the reference rate. The notional amount is not exchanged. It is a cash amount based on the rate differentials and the notional value of the contract.

### Key Takeaways

• Forward rate agreements (FRAs) are over-the-counter (OTC) contracts between parties that determine the rate of interest to be paid on an agreed-upon date in the future.
• The notional amount is not exchanged, but is a cash amount based on the rate differentials and the notional value of the contract.
• A borrower might want to fix their borrowing costs today by entering into an FRA.
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## Formula and Calculation for a Forward Rate Agreement (FRA)

\begin{aligned} &\text{FRAP} = \left ( \frac{ ( R - \text{FRA} ) \times NP \times P }{ Y } \right ) \times \left ( \frac{ 1 }{ 1 + R \times \left (\frac{ P }{ Y } \right ) } \right ) \\ &\textbf{where:} \\ &\text{FRAP} = \text{FRA payment} \\ &\text{FRA} = \text{Forward rate agreement rate, or fixed interest} \\ &\text{rate that will be paid} \\ &R = \text{Reference, or floating interest rate used in} \\ &\text{the contract} \\ &NP = \text{Notional principal, or amount of the loan that} \\ &\text{interest is applied to} \\ &P = \text{Period, or number of days in the contract period} \\ &Y = \text{Number of days in the year based on the correct} \\ &\text{day-count convention for the contract} \\ \end{aligned}

1. Calculate the difference between the forward rate and the floating rate or reference rate.
2. Multiply the rate differential by the notional amount of the contract and by the number of days in the contract. Divide the result by 360 (days).
3. In the second part of the formula, divide the number of days in the contract by 360 and multiply the result by 1 + the reference rate. Then divide the value into 1.
4. Multiply the result from the right side of the formula by the left side of the formula.

Forward rate agreements typically involve two parties exchanging a fixed interest rate for a variable one. The party paying the fixed rate is referred to as the borrower, while the party paying the variable rate is referred to as the lender. The forward rate agreement could have the maturity as long as five years.

A borrower might enter into a forward rate agreement with the goal of locking in an interest rate if the borrower believes rates might rise in the future. In other words, a borrower might want to fix their borrowing costs today by entering into an FRA. The cash difference between the FRA and the reference rate or floating rate is settled on the value date or settlement date.

For example, if the Federal Reserve Bank is in the process of hiking U.S. interest rates, called a monetary tightening cycle, corporations would likely want to fix their borrowing costs before rates rise too dramatically. Also, FRAs are very flexible, and the settlement dates can be tailored to the needs of those involved in the transaction.

## Forward Rate Agreement (FRA) vs. Forward Contract (FWD)

A forward rate agreement is different from a forward contract (FWD). A currency forward is a binding contract in the foreign exchange market that locks in the exchange rate for the purchase or sale of a currency on a future date. A currency forward is a hedging tool that does not involve any up-front payment. The other major benefit of a currency forward is that it can be tailored to a particular amount and delivery period, unlike standardized currency futures.

The FWD can result in the currency exchange being settled, which would include a wire transfer or a settling of the funds into an account. There are times when an offsetting contract is entered, which would be at the prevailing exchange rate. However, offsetting the forward contract results in settling the net difference between the two exchange rates of the contracts. An FRA results in settling the cash difference between the interest rate differentials of the two contracts.

A currency forward settlement can be on either a cash or delivery basis, provided that the option is mutually acceptable and has been specified beforehand in the contract.

## Limitations of Forward Rate Agreements

There is a risk to the borrower if they had to unwind the FRA and the rate in the market had moved adversely so that the borrower would take a loss on the cash settlement. FRAs are very liquid and can be unwound in the market, but there will be a cash difference settled between the FRA rate and the prevailing rate in the market.

## Example of a Forward Rate Agreement

Company A enters into an FRA with Company B in which Company A will receive a fixed (reference) rate of 4% on a principal amount of $5 million in half a year, and the FRA rate will be set at 50 basis points less than that rate. In return, Company B will receive the one-year London Interbank Offered Rate (LIBOR), determined in three years’ time, on the principal amount. The agreement will be settled in cash in a payment made at the beginning of the forward period, discounted by an amount calculated using the contract rate and the contract period. The formula for the FRA payment takes into account five variables: • FRA = the FRA rate • R = the reference rate • NP = the notional principal • P = the period, which is the number of days in the contract period • Y = the number of days in the year based on the correct day-count convention for the contract Assume the following data, and plugging it into the formula above: • FRA = 3.5% • R = 4% • NP =$5 million
• P = 181 days
• Y = 360 days

The FRA payment (FRAP) is thus calculated as:

\begin{aligned} \text{FRAP} &= \left (\frac{ (0.04 - 0.035) \times \5\ \text{Million} \times 181 }{ 360 } \right ) \\ &\quad \times \left ( \frac{ 1 }{ 1 + 0.04 \times \left ( \frac{ 181 }{ 360 } \right ) } \right ) \\ &= \12,569.44 \times 0.980285 \\ &= \12,321.64 \\ \end{aligned}

If the payment amount is positive, then the FRA seller pays this amount to the buyer. Otherwise, the buyer pays the seller. Remember, the day-count convention is typically 360 days in a year. Note also that the notional amount of \$5 million is not exchanged. Instead, the two companies involved in this transaction are using that figure to calculate the interest rate differential.

## What happens if you sell a forward rate agreement (FRA)?

The seller of a forward rate agreement (FRA), or the lender in the transaction, agrees to accept a fixed interest rate at a predetermined future date. If there has been a decrease in the floating market interest rate, then the FRA seller benefits from having locked in the higher rate.

## Why would you buy a forward rate agreement?

The main reason to buy a forward rate agreement (FRA) is to hedge against future increases in interest rates. By locking in an interest rate to be paid at a specified date in the future, FRA purchasers provide themselves with a measure of protection should market rates rise.

## What are the risks of a forward rate agreement?

A forward rate agreement (FRA) is an over-the-counter (OTC) contract, meaning that there are lower levels of regulation and oversight related to the transaction compared with futures contracts. It can sometimes be difficult for a party to close an FRA before the maturity date, and the agreements are also subject to counterparty risk, as there is a potential that a participant in the contract could default on its obligations.

## The Bottom Line

A forward rate agreement (FRA) is an over-the-counter (OTC) contract that establishes an interest rate to be paid at a predetermined future date. The parties in the FRA do not exchange the notional amount. Instead, they settle the contract in cash based on the rate differential and the contract’s notional value.

Parties can enter into an FRA to hedge against or benefit from future interest rate movements. Borrowers can use an FRA to fix their borrowing costs, while lenders can benefit from locking in a predetermined rate in the event that market rates fall.

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