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# Forward Rate Agreement, FRA

By Yuriy Smirnov Ph.D.

## Definition

The forward rate agreement or FRA is an over-the-counter (OTC) cash-settled interest rate derivative. It is a contract between two parties who want to hedge themselves against interest rate risk. Under this agreement, two parties agree to exchange future interest payments based on a specified notional amount. In this case, the first party is liable to make payments to the second party at a specified fixed interest rate, and the second party makes payments to the first party at a floating interest rate called reference rate. LIBOR (London Interbank Offered Rate) and EURIBOR (European Interbank Offered Rate) are most often used as the reference rate.

The buyer (borrower) of a forward rate agreement is holding a long position, and the seller (lender) is holding a short position. Both buyer and seller are hedging against interest rate risk by entering a forward rate agreement, but the buyer is hedging against future rising interest rates, and a seller is hedging against future declining interest rates.

Please also note that no transfer of the notional amount is required under the forward rate agreement!

## Notation

Let’s consider an example of an FRA quote to better understand how to interpret it.

USD 1x7 1.50/1.75%

where:

• USD is the currency of a contract (US dollars in the quote above)
• 1x7 means depositing/borrowing interest starting 1 month from now for 6 months (7-1), and the maturity date is 7 months from now
• 1.50% is the depositing contract rate
• 1.75% is the borrowing contract rate

The difference between the depositing and the borrowing rate is called the bid-ask spread (0.25% in the example above). Under this forward rate agreement, one party may receive payments at a fixed rate of 1.50% and pay at a floating rate or borrow at a fixed rate of 1.75% and receive payments at a floating rate.

The other examples of common FRA notations are listed in the table below.

## Timeline of forward rate agreement

The forward rate agreement has 5 critical dates.

1. Transaction date (usually 2 business days before the spot date)
2. Spot date
3. Fixing date (usually 2 business days before the spot date)
4. Settlement date
5. Maturity date

Let’s consider the example when two parties enter 1x4 FRA on May 10.

As the transaction date is May 10, the spot date is within 2 business days on May 12. The fixed interest rate is locked on the transaction date. The exposure period of 1 month begins on the spot date and ends on the settlement date on June 11. However, the reference rate should be determined 2 business days before the settlement date on June 9 (fixing date). Now, the reference rate can be compared to a contract rate, and one party is liable to pay a settlement amount to the other party on the settlement date.

Actually, the forward rate agreement ends at a settlement date because the settlement amount is paid, and both parties do not have any further contractual engagements. However, the 3-month contract period ends on the maturity date September 11.

## Formula

The formula to calculate the settlement amount (s) under the forward rate agreement is as follows:

 S = P × (rref - rFRA)× t T 1 + rref  × t T

where P is the notional amount (also called principal amount), rref is the reference rate (on an annual basis), rFRA is the contract rate (on an annual basis), t is a contract period in days, and T is a year basis in days (360 for USD and EUR, 365 for GBP).

If the reference rate and the contract rate are already adjusted to a contract period, the formula above should be rewritten as follows:

 S = P × rref - rFRA 1 + rref

Please note that the settlement amount is paid on a settlement date rather than on a maturity date. Therefore, it should be discounted at the reference rate!

As we can see, the settlement amount can have both positive and negative value. How to interpret it?

This depends on whether it is a “payer FRA” (buyer of a contract is paying at a fixed contract rate and receiving at a floating reference rate) or a “receiver FRA” (buyer of a contract is paying at a floating reference rate and receiving at a fixed contract rate).

### Payer FRA

If the reference rate is higher than the contract rate (rref > rFRA), the buyer of a payer FRA receives the settlement amount from the seller. Otherwise, (rref < rFRA) the buyer is liable to pay this amount to the seller.

### Receiver FRA

If the reference rate is lower than the contract rate (rref < rFRA), the buyer of a receiver FRA receives the settlement amount from the seller. Otherwise, (rref > rFRA) the buyer is liable to pay this amount to the seller.

## Calculation example

### Example of hedging with payer FRA

A corporation is going to borrow \$2,000,000 USD in 3 months for a 6-month period. It is possible to borrow this amount today at the current 6-month LIBOR 2.70425% plus 150 basis points. However, it is expected that the 6-month LIBOR will increase to 3.75% in the forthcoming 3 months. The chief financial officer decides to mitigate interest rate risk by buying 3x9 forward rate agreement. A bank gives a quote.

USD 3x9 2.65225/2.75625%

A corporation buys a “payer” FRA for a notional amount of \$2,000,000 USD and a contract rate of 2.75625%.

Let’s assume that on the fixing date the 6-month LIBOR is 3.37821%. As far as the reference rate exceeds the contract rate, the bank has to transfer the settlement amount of \$6,116.29 to a corporation on the settlement date.

 S = \$2,000,000 × (3.37821%-2.75625%)× 180 = \$6,116.29 360 1 + 3.37821%    × 180 360

### Example of hedging with receiver FRA

An insurance company intends to deposit \$10,000,000 USD in 6 months for the 6-month period. The management of a company is going to hedge against decreasing interest rates by buying a “receiver” 6x12 FRA. The quote given by a bank on the transaction date (June 12, 20X8) is as follows:

USD 6x12 1.82324/1.83524%

The 6-month USD LIBOR is used as the reference rate, and the contract rate is 1.82324%.

The spot date will be in 2 business date on June 14, 20X8. Therefore, the settlement date will come in 6 months on December 14, 20X8, and the fixing date in 2 business days before it on December 12, 20X8.

The forward rate agreement matures in 12 months on June 12, 20X9; thus, the contract period is 183 days. Suppose that the 6-month LIBOR fixes at 2.32250% on the fixing date. The settlement amount is \$25,082.92.

 S = \$10,000,000 × (2.32250%-1.82324%)× 183 = \$25,082.92 360 1 + 2.32250%    × 183 360

As far as the reference rate exceeds the contract rate, an insurance company has to transfer \$25,082.92 to a bank on the settlement date.

## Advantages and disadvantages

### Advantages

1. Flexibility. As long as the forward rate agreement is an OTC derivative, the buyer and seller may agree on any notional amount and have a great choice of contract periods depending on the reference rate.
2. No margin requirements.

### Disadvantages

1. Nonsettlement risk. Unlike exchanges where a clearing house guarantees that both seller and buyer get paid, both parties of FRA are exposed to nonsettlement risk.
2. No formal market. Unlike exchange-traded derivatives, FRAs are not standardized. Therefore, it is sometimes very difficult to close an open position by buying or selling an opposite agreement.