# Forward Rate Agreements

## Definition

A forward rate agreement (FRA) is a forward contract between parties that determines the rate of interest, or the currency exchange rate, to be paid or received on an obligation beginning at a future start date.

## Basics

• The long position in an FRA is the party that would borrow money (long the loan, with the contract price being the interest rate on the loan).
• If LIBOR at expiration is above the rate specified in the forward agreement, the long position in the contract can be viewed as the right to borrow at below market rates, and the long will receive a payment.
• If LIBOR at the expiration date is below the FRA rate, the short will receive a cash payment from the long. (The right to lend at above market rates has a positive value.)
• The notation for FRAs is unique. For example, a 2×3 FRA is a contract that expires in two months (60 days), and the underlying loan is settled in three months (90 days). The underlying rate is 1-month (30-day) LIBOR on a 30-day loan in 60 days. A timeline for a 2×3 FRA is shown below.

## Pricing an FRA

The “price” of the FRA is actually the forward interest rate implied by the spot rates consistent with the FRA. For example, the “price” of the 2×3 FRA is the 30-day forward rate in 60 days implied by the 60- and 90-day spot rates.

## Valuing an FRA

The value of an FRA to the long or short position comes from the interest savings on a loan to be made at the settlement date. This value is to be received at the end of the loan, so the value of an FRA after initiation is the present value of these savings. Remember, if the rate in the future is less than the FRA rate, the long is “obligated to borrow” at above-market rates and will have to make a payment to the short. If the market interest rate is greater than the FRA rate, the long will receive a payment from the short.

Lets outline the general steps for valuing a 2×3 FRA (a 30-day loan in 60 days) 40 days after initiation (which means there are 20 days remaining until the FRA expires).

1. Step 1: Calculate the implied 30-day forward rate at the settlement date, 20 days from now, using the current 20-day spot rate and the current 50-day spot rate. Basically, this calculates a new FRA rate (same loan term as the original one) if it is imitated today.
2. Step 2: Calculate the value of the FRA at maturity as the notional principal times the difference between the forward rate from Step 1 and the original FRA “price.” Make sure to convert from an annual rate to a 30-day rate. If the current forward rate is greater than the original FRA price, the long position has positive value. If the current forward rate is less than the original FRA price, the short position has positive value.
3. Step 3: Calculate the value of the FRA today by discounting the value at maturity from Step 2 at the 50-day spot rate.