| Математика
Key words: Forward rate agreement (FRA), FRAs quoting terminology, “borrowing” funds, FRA mechanics

FRA (forward rate agreement) is an OTC (over-the-counter) contract that guarantees a borrowing or lending rate for a future period based on a given notional principal amount.
Usually, the reference rate used in the FRA is the same as the actual borrowing rate of the borrower. The basis for the reference rate is agreed upon on the trade date and usually, for the main currencies, the LIBOR calculated by British Bankers Association is used.

When one buys a FRA one is “borrowing” funds. This differs from interest rate futures, where “buying” is lending funds:

If you think interest rate will rise buy FRAs or sell futures and vice versa.

The terminology quoting FRAs refers to the borrowing time period and the time at which the FRA matures.
A three-month loan beginning in three months time is a 3 × 6 FRA.

FRAs are available for a variety of periods, starting from a few days to terms of several years.
In practice, for the standard periods like 3, 6 and 12 months market liquidity is the highest. Generally an FRA with for example 5-months period can be traded.

The principal amount is not exchanged and there is no obligation by either party to borrow or lend capital in the future.
Therefore, notional principal amount is simply the amount on which interest payment is calculated.

The value of a FRA at inception is zero and thus there is no exchange of cash at the time of the trade.
Only the payment that arises as a result of the difference in interest rates changes hands:

– A buyer taking a long FRA position intends to profit from the LIBOR rate at the beginning of the forward period being higher than expected.

– A seller taking a short FRA position intends to profit from the LIBOR rate at the beginning of the forward period being lower than expected.

FRA mechanics and standard terms

Notional / Principal: The amount for which the FRA is traded.
Trade date: The date of the deal
Spot date: The Spot date is used to determine the settlement date and is usually two business days after the trade date.
Fixing date: The date on which the reference rate is determined
Settlement date: The date when the settlement amount is paid. The settlement date is the time period after the spot date referred to by the FRA terms, for example, a 2 × 4 FRA has a settlement date two calendar month after the spot date.
Maturity: The date on which the notional loan expires.

FRA contracts

FRA pricing

Consider a case where a bank has sold $500 million notional of a 5×8 FRA at 5.8% LIBOR rate.
If the market rate is 5.1% on the fixing date and the contract period is 90 days the contract will result in a profit of $873 583.

FRA pricing

1. On the fixing date (5 months have passed), we can deposit $500 MM for three months (90 days) at 5.8% LIBOR rate, but the money market offers only 5.1%.

2. On the maturity date (8 months passed), if we theoretically deposited $500 MM @5.8% we would have (5.8%-5.1%)*90/360*$500 ММ or $884 722 more than if we deposited @5.1%.

3. But if we know on the fixing date that we will receive $884 722 on the maturity date we can easily calculate NPV on the fixing date taking into account the current annual LIBOR rate @5.1% : $884 722 / (1+5.1%*90/360)=$873 583. This is the profit that our bank will receive from the FRA buyer on the settlement date.

FRAs are not marked to market, therefore profit or loss accumulates over time until fixing date.
Since gains in a FRA can become quite substantial before the settlement date, the losing counterparty may fail to make the required payment on the settlement date.
Therefore, there is a relative large credit risk to be taken into account as well as the credit quality of many different potential counterparties.