**Derivatives**

**Reading 49. Basics of Derivative Pricing and Valuation**

**Learning Outcome Statements**

e. define a forward rate agreement and describe its uses;

*CFA Curriculum, 2020, Volume 6*

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### Subject 4. Forward Rate Agreements

**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.

*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 Contributed Comments**
7

You need to log in first to add your 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