# Forward Rate Agreement

A forward rate agreement ( FRA ) is an off-market interest rate futures ( derivative), which makes it possible to secure an interest rate for a date in the future investment period.

The agreement covers not the actual investment or consumption, it is agreed only an exchange of interest payments. Based on the market price of risk, however, an FRA is substantially equivalent to the agreement of a date in the future investment or consumption.

The buyer of an FRA secures the interest rate for borrowing money. He thus secured against rising interest rates and waived off for the savings opportunities that falling interest rates. The position of the seller is an exact mirror image.

The FRA the analog business on futures exchanges is the money market futures.

## Operation

The agreement of a FRA essentially comprises the following components:

- The time of beginning of a date in the future, fictional borrowing t1
- The duration of the notional borrowing t2 ( investment period )
- The amount of the notional borrowing N ( the nominal )
- The agreed interest rate f ( FRA rate or forward rate) for future investment period
- A reference rate for the same investment period, typically a money market rate as (depending on currency) the Libor or Euribor.

The total term of the transaction t3 t2 is the sum of lead time t1 and investment period. FRA will often see pros and total run time, so FRA 3x9 for a FRA with a lead time of 3 months t1 and t2 an investment period of 6 months.

After the lead-time the level of the reference rate is determined ( " fixed "). The buyer of the FRA receives from the seller the reference rate based on the notional N for the investment period t2 and in return pays the agreed FRA rate for N and t2 to the seller. In fact, do not pay both parties, but it is only the difference between the agreed FRA rate and the reference rate gefixtem balanced.

Since the buyer is usually able to borrow at the reference rate on the money market, it can be secured with the FRA in advance a refinancing rate: The interest expense for the time t1 made borrowing money it receives from the FRA by the seller, so that the FRA rate than him refinancing rate remains. Similarly, the seller may represent an investment for FRA rate. The eventual completion of an associated money market business is not mandatory for any of the parties.

Normally, interest payments are in arrears, so that would also be paying off the FRA at time t3. In fact, the compensation is already made at the end of the lead time (t1 ), the amount to be paid over the period t2 is discounted. The counterparty risk of the FRA is therefore only relevant in the period up to the end of the lead time.

## Example

Bank A Bank B buys a FRA. Both the lead-time (t1 ) and the investment period (t2 ) should be 3 months. It is a 3x6 FRA. The business starts February 28. The nominal (N) amounts to EUR 100 million.

On the financial statements of the 3 - month interest rate amounts to 1.6%, the 6- Monatsszins 2.4%. This results in a fair forward rate of 3.187, which is agreed to as FRA rate f.

The forward rate of 3.187% calculated as follows:

At the end of the preliminary period, ie on May 31, the FRA rate of 3.187% with the then three - month interest rate is compared. This amounts to 2.4%. Bank A to Bank B as the buyer must thus a compensation payment of 3.187% - 2.4 % = 0.787 %, based on EUR 100 million pay for 3 months, ie 196 750 EUR. As this amount is not paid in arrears at the end of the investment period 31 August, but now, he still has to be discounted at the current 3- month interest rate: A bank that is actually paid 195,576 EUR.

Bank A borrows now additionally on May 31 on the money market EUR 100 million for 3 months, she has to at the end of the term of August 31, 2.4% or 600,000 EUR to pay in interest. Together with the cost of the FRA, these are 796,750 EUR, which based on the notional amount of EUR 100 million for a quarter corresponds exactly to the agreed FRA interest rate of 3.187%. Bank A has therefore secured a borrowing at that rate.

## Calculation

The value of FRAs can be calculated analogously to the value of a futures contract. A decisive factor is the runtime, the specified base rate, the related development of reference interest rates and the agreed volume.

## History and economic importance

FRAs are classic instruments of financial management. It is a short-term instrument, the liquid is up to one year. Their use was widespread especially in the second half of the 1980s and during the 1990 years and were at this time under the interest rate swap, the second most important OTC interest rate derivative. In recent years, the importance of FRAs, however, has been greatly reduced. The global share of FRAs to the entire OTC interest rate derivatives has, according to the Bank for International Settlements ( BIS) between 1998 and 2007 almost halved from 11.5% to only 6.6 %.

## Comments

- Interest income
- Futures
- Banking
- Finance