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Forward Rate Agreement (FRA)

On February 18, 2008, in definition & usage, Derivatives, by admin

What is it ?

A contract made directly between 2 parties (a seller and a buyer) fixing the interest rate (at settlement date) that will apply to a notional principal sum of money for an agreed future time period (maturity date)

Such that at maturity date,

  • The FRA buyer: receives money from the seller if the reference benchmark interest rate is above the one agreed in the contract.
  • The FRA seller: receives money from the buyer if the reference benchmark interest rate is bellow the one agreed in the contract.

The notional principal never changes hands.

FRA should not be confounded with forward rate implied from yield to maturity bond. In that case there is no specific agreement and we don’t talk about FRA.

Who ?

  • Over-the-counter (OTC) transactions.
  • A FRA buyer could be a corporate borrower who fears a rise of interest rate and wants to be hedged.
  • A FRA seller could be an investor who fears the decline of interest rate and wants to be hedged.

Hedging against interest rate change can reduce the volatility of a company’s earning or debt. This could affect positively its share price.

Rights and obligations ?

  • The seller must pay if the interest rate turns out to be above the contractual rate.
  • The buyer must pay if the interest rate turns out to be bellow the contractual rate: he can secure an interest rate but he cannot gain if the rate turns out to be lower than initially feared.

Risks ?

The risk is that one party to the deal may default on its contractual obligations.

Example

Let us assume the following FRA :

Notional principal:€100 million
Deal Type:Client buys FRA
Contract rate:4% p.a.
Start date:today
Settlement date:in 6 months
Maturity date:in 12 months
Contract period:A 6 months period starting in 6 months
reference rate:6-month euros EURIBOR

Such a deal would be noted 6v12 or 6×12

The FRA dealer will pay the client if the 6-month euros Euribor rate is above 4%.

The client will pay the dealer if the 6-month euros Euribor rate is below 4%.

Payment will be based upon notional of 100 MEUR.

The reference euribor rate will be taken at the settlement date : at that time both parties will know who should pay whom

a) if the rate is 5% p.a.(that is above the contractual rate), the dealer will pay to the client at maturity date:

100 MEUR * (5% – 4%) * 6/12 = 0.5 MEUR.

Now let’s suppose that the client borrowed the money at Euribor rate + 0.5% p.a. bank margin.

The interest is :

100 MEUR * (5% + 0.5%) * 6/12 =2.75 MEUR
Less: compensation from the dealer0.5 MEUR
Net cost of borrowing2.25 MEUR

Effective rate: 2.25 / (100 * 6/12) = 4.5%

Note: in reality, to reduce credit risk, the compensation is paid at settlement date and is discounted back at Euribor rate so that nothing happens at maturity date.

amount paid at settlement date: 0.5 MEUR / (1 + 5% *(6/12)) = 0.487 MEUR

b) if the rate is 3% p.a. (that is bellow the contractual rate),

the  client will pay to the dealer at maturity date:

100 MEUR * (4% – 3%) * 6/12 = 0.5 MEUR.

Let us suppose that the client borrowed the money at Euribor rate + 0.5% p.a. bank margin.

The interest is :

100 MEUR * (3% + 0.5%) * 6/12 =1.75 MEUR
Add: compensation paid to the dealer0.5 MEUR
Net cost of borrowing2.25 MEUR

Effective rate: 2.25 / (100 * 6/12) = 4.5%

Note: in reality, to reduce credit risk, the compensation is paid at settlement date and is discounted back at Euribor rate so that nothing happens at maturity date.

amount paid at settlement date: 0.5 MEUR / (1 + 3% *(6/12)) = 0.493 MEUR

To summarize as a graphic for the client:

How could a FRA dealer fix the rate ?

Based on the assumption that arbitrage opportunities should not be available in an active and efficient market.

For example, the following process should not be possible:

- A FRA Dealer could borrow today 1 MEUR at 5% for 1 year: the cost being 1MEUR*5%*1=0.05 MEUR

- He could deposit today those 1 MEUR at 4% for 6 months and get an Interest of 1MEUR * 4% *(6/12)=0.02 MEUR

- He could sell a 6v12 FRA at 10.5% with a notional sum of 1.02 MEUR and deposit in 6 months the 1 MEUR +0.02 MEUR @(Euribor-0.5%spread) and his gain would be:

1.02 MEUR*(10.5%-0.5%)*(6/12)=0.051 MEUR

The net gain is 0.051 – 0.05 = 0.001 MEUR without any risk

If the market is efficient, the dealer could not sell his FRA at 10.5%

The FRA are most of the time based upon interest rate futures that are actively traded or Libor/Euribor rate .

Premium paid by the parties

Let us take a given FRA. There is a 50/50 chance that the market rate at settlement date is above or below the agreed contractual rate. Both the buyer or the seller have a 50% chance of making money on the deal. Therefore, neither party should pay a premium to the other to enter into the forward contract.

Discussion

FRA seen as a swap

A FRA can be seen as a sort of “one time” swap: to illustrate that, now let’s consider the above example

One leg: The client pays the contractual rate (4% p.a.) applied to 100 MEUR to the FRA dealer that is to say 100 MEUR * 4% *(6/12)= 2 MEUR

Other leg: The FRA dealer pays the client the Euribor rate (Let us take 5%) applied to 100 MEUR that is to say 100 MEUR * 5% *(6/12)= 2.5 MEUR

Netted out; the dealer owes the client 0.5 MEUR (or 0.487 MEUR if the payment is made at settlement date)

The rate for the client applied to the same notional sum (100 MEUR) is

- 4% + Euribor – (Euribor +0.5%) = – 4.5%

General formulation

Let’s consider a FRA between company A and company B and let’s note

Rcontract : the rate of interest agreed to in the FRA

NP : the notional principal underlying the contract

T1 : the settlement date

T2 : the maturity date

RM : the actual spot interest rate observed in the market at time T1 for the period between T1 and T2

The contract date is today. Of course, the times T1 and T2 are expressed in a proper unit coherent with the rates Rcontract and RM as seen in the example above.

The FRA is such that it could be represented by the following flowchart between company A and B :

In T2 the amount that will be paid by Company A or B is

As already mentioned in reality, the FRA is settled at time T1 rather than T2. The payoff must be discounted back:

Hedging and spread for a FRA Dealer

The dealer can “guess” the evolution of the interest rate. If a dealer sold the FRA in the example above he is at risk. So he needs to be hedged:

- He could buy an interest rate Future

- He could buy a FRA covering the one he sold

Let us illustrate that with the same example as above: the dealer sold a 6v12 FRA (4% p.a.) – 100 MEUR to a client

At the same time (or as soon as possible), the dealer will buy a 6v12 FRA (3.95%) – 100 MEUR from a fund manager who is worried that the fall of interest rate will reduce the return of his fund.

This will give the following situation based upon the same notional sum

The difference between the rate received by the dealer from the client and paid by the dealer to the fund manager is the dealer’s spread (here 5 basis point).

 

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