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##### Subject 3. Forward Rate Agreements

A forward rate agreement (FRA) is a forward contract in which one party, the long, agrees to pay a fixed interest payment at a future date and receive an interest payment at a rate to be determined at expiration. It is a forward contract on an interest rate (not on a bond or a loan).

• The long pays fixed rate and receives floating rate. If Libor rises the long will gain.
• The short pays floating rate and receives fixed rate. If Libor falls the short will gain.

The fixed rate is also called the forward contract rate. The interest rate to be determined at expiration is also called the underlying rate. The buyer effectively has agreed to borrow an amount of money in the future at the stated forward (contract) rate. The seller has effectively locked in a lending rate. The buyer of a FRA profits from an increase in interest rates. The seller of a FRA profits from a decline in rates.<

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Example

Shell and Barclays enters into the following FRA:

• Shell, the end user, takes a long position in a FRA that expires in 30 days and is based on 60-day LIBOR.
• Barclays, a dealer, quotes a rate of 5.65% for this FRA.
• The notional principal of this FRA is \$1,000,000.

By convention, this FRA is also referred to as a 1 x 3. At the expiration of the FRA in 30 days:

• Shell pays a fixed rate of 5.65% immediately.
• Barclays promises to pay a rate of 60-day LIBOR determined at expiration. Suppose that the 60-day LIBOR at expiration is 6%. Barclays will pay 6% of interest to Shell 60 days after the contract expiration date. In effect, the 6% interest is paid 90 days (30 + 60) from the contract initiation date.

Note the market convention quotes the time periods as months, but the calculations use days based on the assumptions of 30 days in a months. For example, a "1 x 3 FRA" expires in 30 days, and the payoff of the FRA is determined by 60-day Libor when the FRA expires in 30 days.

User Comment
Seemorr So you're not paying the absolute difference between the two rates ... you're paying the percentage difference.
Gooner7 those 2 numbers are the same thing
jpducros note that expiration date = t1, not t2
freyalam t2 is when payments are made
(page 43, vol 6, the CFA institute textbook, for level 1)
SCBAnalyst t1 amount of payment is determined for actual payment in t2- hence the discounting
johntan1979 In Example 1, Shell receives a profit of \$577.56
ankurwa10 as i understand, from the perspective of an end-user (long party)

formula: (( underlying rate - agreed rate) ) x number of days to maturity/360) / 1+ underlying rate x number of days until maturity/360

Explanation:

Numerator: If interest rate rises (e.g. LIBOR is 6% and agreed rate is 5%, I make money); so calculate the differential i.e. 6% - 5% but then have to adjust the LIBOR for days until maturity.

Denominator: have to discount the amount by LIBOR discount, because we are agreeing to receive an interest amount relative to LIBOR, IN THE FUTURE.

Don't know if this is accurate though :P 