# Forward Rate Agreements and Calculating FRA Payments

Forward Rate Agreements (FRA’s) are similar to forward contracts where one party agrees to borrow or lend a certain amount of money at a fixed rate on a pre-specified future date.

For example, two parties can enter into an agreement to borrow $1 million after 60 days for a period of 90 days, at say 5%. This means that the settlement date is after 60 days, on which date the money will be borrowed/lent for a period of 90 days.

The party that is borrowing money under the FRA has a long position, and the party that is lending money has a short position in the FRA.

FRA contracts are usually cash-settled, that is, the money is not actually lent or borrowed. Instead, the forward rate specified in the FRA is compared with the current LIBOR rate. If the current LIBOR is greater that the FRA rate, then the long is effectively able to borrow at a below market rate. The long will therefore receive a payment based on the difference between the two rates. If, however, the current LIBOR was lower than the FRA rate, then long will make a payment to the short. The payment ends up compensating for any change in interest rates since the contract date.

FRAs can be based on different periods, and are quoted in terms of months to settlement date and the months to completion of interest period. In our example, the settlement date is after 60 days (2 months), and then there is an interest period of 90 days (3 months). The contract will complete after a total of 2+3 = 5 months. This FRA will be referred to as 2x5 FRA.

FRAs are generally used to lock in an interest rate for transactions that will take place in the future. For example, a bank that plans to issue or roll over certificates of deposit, but anticipates that interest rates are headed upward, can lock in today’s rate by purchasing FRA. If rates do rise, then the payment received on the FRA should offset the increased interest cost on the CDs. If rates fall, the bank pays out.

The above example demonstrated how FRAs are used to lock in an interest rate or debt cost. FRA’s can also be used to lock in the price of a short-term security to be bought or sold in the near future.

- If the investment is being purchased, you can hedge the risk that interest rates may fall (which would increase the price of the investment) by selling the FRA.
- If the investment is being sold, you can hedge against the risk of rates rising (which would depress the sales price of the security) by buying the FRA.

**Calculating FRA Payments**

Let’s take an example to understand how payments in an FRA are calculated.

Consider a 3x6 FRA on a notional principle amount of $1million. The FRA rate is 6%. The FRA settlement date is after 3 months (90 days) and the settlement is based on a 90 day LIBOR.

Assume that on the settlement date, the actual 90-day LIBOR is 8%. This means that the long is able to borrow at a rate of 6% under the FRA, which is 2% less than the market rate. This is a saving of:

\= 1,000,000 * 2% *90/360 = $5,000

This is the interest that the long would save by using the FRA. Since the settlement is happening today, the payment will be equal to the present value of these savings. The discount rate will be the current LIBOR rate.

FRA Payment = $5,000/(1+0.08)^(90/360) = $4,904.72

#### Course Downloads

- Introduction to Forward Contracts
- Forward Contracts – Settlement/Default Risk (T-bill Example)
- How is a Forward Contract Settled?
- Forward Contract Termination Prior to Expiry
- End-user Vs. Dealers in a Forward Contract
- How Equity Forward Contracts Work?
- Forward Contracts on Zero-coupon and Coupon Bonds
- How are LIBOR and EURIBOR Calculated?
- Forward Rate Agreements and Calculating FRA Payments
- How Currency Forward Contracts Work?

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