Forward Rate Agreement

A Forward Rate Agreement (FRA) is an over-the-counter interest rate futures contract ( derivative ) that enables you to hedge an interest rate for a future investment period.

The agreement does not include the actual investment or borrowing, only an exchange of interest payments is agreed. In terms of market price risk, however, an FRA is essentially equivalent to agreeing to invest or borrow money in the future. The corresponding transaction type of a transaction involving a real investment or borrowing in the future is called a forward-forward deposit .

The buyer of an FRA secures the interest for a borrowing. In doing so, he protects himself against rising interest rates and foregoing the savings that falling interest rates offer. The position of the seller is exactly the mirror image.

That the FRA analog business on futures exchanges is the money market - Future .

functionality

The agreement of an FRA essentially comprises the following components:

• The time of the start of a fictitious borrowing t ₁ in the future
• The duration of the fictitious borrowing t ₂ (investment period)
• The amount of notional borrowing N (the nominal )
• The agreed interest rate f (FRA rate or forward interest rate ) for the future investment period
• A reference interest rate for the same investment period, typically a money market rate such as Libor or Euribor (depending on the currency) .

The total duration of the transaction t ₃ is the sum of the lead time t ₁ and the investment period t ₂ . FRA are often referred to as lead time and total lead time, i.e. FRA 3x9 for an FRA with a lead time t ₁ of 3 months and an investment period t ₂ of 6 months.

After the lead time has expired, the level of the reference interest rate is determined (" fixed "). The buyer of the FRA receives from the seller the reference interest rate based on the nominal N for the investment period t ₂ and in return pays the agreed FRA rate for N and t ₂ to the seller. In fact, both parties do not pay, only the difference between the agreed FRA rate and the fixed reference interest rate is settled.

Since the buyer can normally refinance himself at the reference interest rate on the money market , he can secure a refinancing rate in advance with the FRA: he receives the interest expense for a borrowing made at time t ₁ from the FRA from the seller, so that the FRA rate is transferred to him remains as the refinancing rate. Similarly, the seller can represent an investment at the FRA rate. The possible conclusion of an associated money market transaction is not mandatory for either party.

Interest payments are normally made in arrears, so that the payment from the FRA would also have to be made at time t ₃ . In fact, the compensation is already carried out at the end of the lead time (t ₁ ), the amount to be paid being discounted over the period t ₂ . The FRA's counterparty risk is therefore only relevant in the period up to the end of the lead time.

example

Bank A buys an FRA from bank B. Both the lead time (t ₁ ) and the investment period (t ₂ ) should be 3 months. So it is a FRA 3x6. Business starts on February 28th. The nominal (N) is EUR 100 million.

At the conclusion of the transaction, the 3-month interest rate is 1.6%, the 6-month interest rate 2.4%. This results in a fair interest rate of 3.187, which is also agreed as FRA rate f.

The forward rate of 3.187% is calculated as follows:

${\displaystyle {\begin{array}{rcl}\left(1+0{,}024\times {\frac {180}{360}}\right)&=&\left(1+0{,}016\times {\frac {90}{360}}\right)\times \left(1+f\times {\frac {90}{360}}\right)\\[1ex]\Leftrightarrow \left({\frac {253}{251}}\right)&=&\left(1+f\times {\frac {90}{360}}\right)\\[1ex]\Rightarrow f&=&0{,}03187=3{,}187\,\%\end{array}}}$

At the end of the lead-up period, i.e. on May 31, the FRA rate of 3.187% is compared with the then current 3-month interest rate. This is 2.4%. Bank A as the buyer must therefore make a compensation payment of 3.187% - 2.4% = 0.787% based on 100 million EUR for 3 months, i.e. 196,750 EUR. Since this amount is not paid in arrears at the end of the investment period on August 31, but immediately, it still has to be discounted using the current 3-month interest rate: Bank A actually pays EUR 195,576.

If bank A now borrows an additional EUR 100 million on the money market for 3 months on May 31, it must pay 2.4% or EUR 600,000 in interest at the end of the term on August 31. Together with the costs from the FRA, this amounts to EUR 795,576, which for a quarter of the year based on the nominal of EUR 100 million corresponds exactly to the interest rate of 3.187% agreed in the FRA. Bank A has therefore secured a borrowing at this rate.

calculation

The value of FRAs can be calculated analogously to the value of a future . The decisive factor is the term, the fixed base rate, the corresponding development of the reference interest rate and the agreed volume.

History and economic importance

FRAs are classic instruments of financial management . It is a short-term instrument that is liquid for up to a year. Their use was particularly widespread in the second half of the 1980s and 1990s, and during this time they were the second most important OTC interest rate derivative after the interest rate swap . In recent years, however, the importance of FRAs has decreased significantly. According to the Bank for International Settlements (BIS), the worldwide share of FRAs in total OTC interest rate derivatives almost halved between 1998 and 2007 from 11.5% to just 6.6%.

Individual evidence

1. ↑ Bernd Rudolph, Klaus Schäfer: Derivative financial market instruments . Springer, Heidelberg 2010, ISBN 978-3-540-79413-4 , pp. 127-130 .

Remarks

1. ↑ As usual, all interest rates are based on the year ( pa ).
2. ↑ This so-called fixing usually takes place 2 business days before the end of the lead-up period.