# Level 1 CFA® Exam:

Forward Rate Agreement

In this lesson, we are going to discuss forward contracts on interest rates called forward rate agreements (FRAs).

A forward rate agreement (FRA) is an agreement made to fix an interest rate at a specified level at a specified future time. With an FRA, it is possible to hedge against the risk of future interest rate changes.

Let us start with a definition of a Eurodollar time deposit. A Eurodollar is a type of deposit offered by banks from outside the United States but denominated in U.S. dollars. The lending rate for Eurodollar deposits is London Interbank Offered Rate (aka. LIBOR) which, thanks to its specific features, is considered to be the most representative rate.

LIBOR is calculated each day by Thomson Reuters, to whom major banks submit their cost of borrowing unsecured funds for 15 periods of time ranging from overnight to 12 months in 10 currencies. So, 150 different LIBOR rates are published every day. LIBOR is quoted as an annualized rate based on a 360-day year assumption. Only in the case of British pounds the year is assumed to have 365 days. LIBOR is very often the underlying asset for FRAs.

### Add-On Interest

There is one more important thing you need to know – in the case of the Eurodollar market, interest is added on to the face value of a contract, which, unsurprisingly, is called add-on interest.

When an investor must repay a 1 million dollar loan taken out for 60 days and based on LIBOR (and 60-day rate is 5%), the interest is calculated as follows:

\(\text{interest}=1,000,000\times5\%\times\frac{60}{360}=8,333\)

The borrower must repay the amount of the loan plus interest, which makes altogether USD 1,008,333.

Back to reference rates. There are two types of reference rates for loans denominated in euros: EURIBOR (Europe Interbank Offered Rate) published by the European Central Bank and EuroLIBOR published by the British Bankers Association. EURIBOR is more popular.

Both LIBOR and EURIBOR are quoted for many different terms and are used as reference rates for loans of various lengths. For example, we can talk about 30-day LIBOR, 90-day EURIBOR, etc.

A forward rate agreement (FRA) is a specific type of forward contract. It is an agreement to fix an interest rate at a specified level at a specified future time. Unsurprisingly, it is businesses and banks that are mostly interested in FRAs. When running a large-scale business, it often happens that you know you are going to make a deposit or take out a loan at some future time. With an FRA you can hedge against the risk of future interest rate changes.

As it is the case with forward contracts, there are two positions a party can take in an FRA:

- the long and
- the short position.

The party that goes long is the one that seeks to take out a loan in the future at a specified interest rate and wants to avoid an increase in rates. Suppose that the future market value of the reference rate underlying the contract (e.g. LIBOR) goes above the forward contract rate. If we are the party going long, we effectively borrow money at a rate lower than market rates. In terms of cash settlement, as the party going long, it is we who receive a payoff.

The party that goes short, on the other hand, is the one that lends money (or makes a deposit) and wants to hedge against a drop in interest rates. If the future market value of the reference rate underlying the contract falls below the forward contract rate, as the short, we will effectively lend money at a rate higher than market rates.

Let us have a look at the payoff formula for the party going long in the contract.

IMPORTANT! This formula is no longer required in your CFA level 1 exam, however it still worth knowing.

\(FRA_{p} = NP\times [\frac{(r_{exp} - r_{forward})\times (\frac{n}{360})}{1 + r_{exp}\times (\frac{n}{360})}]\)

- \(FRA_{p}\) - FRA payoff (long position)
- \(NP\) - notional principal
- \(r_{exp}\) - underlying rate at expiration
- \(r_{forward}\) - forward contract rate
- \(n\) - days in underlying rate

(...)

Another thing we should remember is the specific notation of FRAs. For example:

- a 3x6 FRA means a contract that expires in 90 days (3 times 30 days), and the interest on the loan is paid in another 3 months, i.e. in 180 days (6 times 30 days) from the initiation of the contract. This contract is therefore based on 90-day LIBOR.
- a 12x24 FRA means a contract that expires in 360 days (12 times 30 days), and the interest on the loan is paid in another 12 months, that is in 720 days (24 times 30 days) from the initiation of the contract. This contract is therefore based on 360-day LIBOR.

Example 2

Real FRA: 3 × 9 FRA (long position)

Synthetic FRA:

- short position in 3-month Eurodollar time deposit and
- long position in 9-month Eurodollar time deposit

Example 3

(...)

- Forward rate agreements are interest rate forward contracts.
- A long position in an FRA generates a profit when interest rates rise. Therefore you will want to be the party going long if you are afraid that interest rates may increase, for example when planning to borrow a certain sum of money in the future. After interest rates rise, the short will pay you the difference between the market rate and the forward contract rate.
- The seller, so the party going short, earns when interest rates fall. You will therefore go short if you are afraid of the decrease in interest rates, for example when planning to make a deposit or lend some money in the future. If interest rates happen to fall, the party going long will pay you the difference between the forward contract rate and the market rate.