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A forward rate agreement (FRA) is a cash-settled over-the-counter (OTC) contract between two counterparties, where the buyer is borrowing (and the seller is lending) a notional sum at a fixed interest rate (the FRA rate) and for a specified period starting at an agreed date in the future.
The purpose of FRA is to lock in borrowing or a lending rate for some time in the future. Typically, it involves two parties exchanging a fixed interest rate for a floating rate.
The FRA buyer enters into the contract to protect itself from a future increase in interest rates; the seller of the FRA wants to protect itself from a future decline in interest rates.
FRAs are denoted in the form of “X × Y,” where X and Y are months. So, a 1 × 4 FRA is called “1 by 4”.
Implying that:
A 1 × 4 FRA expires in 30 days (one month), and the theoretical loan is for a time period of the difference between 1 and 4 (three months = 90 days). That is, a three-month Libor determines the FRA’s payoff, but the FRA expires in one month.
A 3 × 9 FRA refers to:
A. A 90-day LIBOR loan starting 270 days from now.
B. A 270-day LIBOR loan starting 90 days from now.
C. A 180-day LIBOR loan starting 90 days from now.
The correct answer is C.
3-by-9 means a 180-day LIBOR loan starting 90 days from now.
The forward rate specified in the FRA is compared with the current LIBOR rate, where:
Suppose we have a 1 x 4 FRA with a notional principal of $1 million. At contract expiration, the 90-day LIBOR at settlement is 6% and the contract rate is 5.5%.
Calculate the value of the FRA at maturity.
$$\text{Payment to the Long}=\text{Notional principal}\ \times\frac{\text{Rate at settlement}-\text{FRA rate}\times\frac{\text{Days}}{360}}{1+\text{Rate at settlement}\ \times\frac{\text{Days}}{360}}$$
Since the settlement rate is higher (6%) than the contract rate (5.5%), the buyer will be receiving money from the seller. The payment to the long at settlement are as follow:
Interest saving:
$$=(6\%-5.5\%)\times\frac{90}{360}\times1\text{m}=1,250$$
Discounted back 90 days @ 6%:
$$=\frac{1,250}{[1+\frac{90}{360}\times6\%]}={1,231.53}$$
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