**CFA Level 1 - Derivatives**

An FRA is a contract in which the underlying rate is simply an interest payment, not a bond or time deposit, made in dollars, euribor or any other currency at a rate that is appropriate for that currency. A forward rate agreement is a forward contact on a short-term interest rate, usually LIBOR, in which cash flow obligations at maturity are calculated on a notional amount and based on the difference between a predetermined

Let's set up the transaction:

In the numerator, we see that the contract is paying the difference between the actual rate that exists in the marketplace on the expiration date and the agreed-upon rate at the beginning of the contract. It is adjusted for the fact that the rate applies to a 180-day rate multiplied by the notional amount.

The divisor is there because when the rates are quoted in the market, they are based on the assumption that they will accrue interest, which will be paid at a certain time. So the FRA payoff needs to be adjusted to reflect the fact that the rate implies a payment that will occur in the future, say 180 days using our above example. Discounting the payment at the current LIBOR does the adjustment.

*forward rate*and the market rate prevailing on that date. The settlement date of an FRA is the date on which cash flow obligations are determined.- The structure is the same for all currencies.
- FRAs mature in a certain number of days and are based on a rate that applies to an instrument maturing in a certain number of days, measured from the maturity of the FRA.
- The structure is as follows: The short party or dealer and the long party or end-user will agree on an interest rate, a time interval and a "hypothetical" contract amount. The end-user benefits if rates increase (she has locked-in a lower rate with the dealer). Because the end-user is long, the dealer must be short the interest rate and will benefit if rates decrease.
- The contact covers a notional amount but only interest rate payments on that amount are considered.
- It is important to note that even though the FRA may settle in fewer days than the underlying rate (i.e. the number of days to maturity in the underlying instrument), the rate that the dealer quotes has to be evaluated in relation to the underlying rate.
- Because there are two-day figures in the quotes, participants have come up with a system of quotes such as 3 x 9, which means the contract expires in three months and in six months, or the nine months from the formation of the contract, interest will be paid on the underlying Eurodollar time deposit upon which the contract's rate is based.
- Other examples include 1 x 3 with the contract expiring in one month based on a 60-day LIBOR, or 6 x 12, which means the contract expires in six months based on the underlying rate of a 180 day LIBOR.
- Usually based on exact months such as 30 day LIBOR or 60 day LIBOR not 37 days and 134 day LIBOR. If a client wants to tailor an FRA, it is likely that a dealer will do it for the client. When this occurs, it is considered to bean
**off-the-run**contract - The best way to see it is through an example, which we will cover in the next section.

**Calculation of Payment at Expiration of FRA**Let's set up the transaction:

- Dealer quotes a rate of 4% on this instrument and end user agrees. He is hoping that rates will increase.
- Expiration is in 90 days.
- The notional amount is $ 5 million.
- The underlying interest rate is the 180 LIBOR time deposit.
- In 90 days the 180-day LIBOR is at 5%. That 5% interest will be paid 180 days later.

So: 5,000,000 ((0.05 - 0.04) (180/360))= $ 47,600

1 + 0.05 (180/360)

Because rates increased, the long party or the end user will receive $47,600 from the short party or the dealer.

If the rates were to decrease, the long party or the end user would have to pony up a payment that would be the difference between the quoted rate and the 180-day LIBOR rate.

In written terms, the formula looks like this for the party going long:

Formula 16.1 ( (Underlying rate at expiration - Forward contract rate)(days in underlying rate/360))1 + underlying rate (days in underlying rate/360) |

- Forward contract rate = rate the two parties agree will be paid
- Days in underlying rate = number of days to maturity on the underlying instrument

In the numerator, we see that the contract is paying the difference between the actual rate that exists in the marketplace on the expiration date and the agreed-upon rate at the beginning of the contract. It is adjusted for the fact that the rate applies to a 180-day rate multiplied by the notional amount.

The divisor is there because when the rates are quoted in the market, they are based on the assumption that they will accrue interest, which will be paid at a certain time. So the FRA payoff needs to be adjusted to reflect the fact that the rate implies a payment that will occur in the future, say 180 days using our above example. Discounting the payment at the current LIBOR does the adjustment.

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