Forward Rate Agreement Calculation

Please find the attached forward rate agreement explained with examples …

Forward Rate Agreement


Basics: A Forward Rate Agreement (FRA) is an agreement between two parties that determines the forward interest rate that will apply to an agreed notional principal (loan or deposit amount) for a specified period.


FRAs are basically OTC equivalents of exchange traded short date interest rate futures, customized to meet specific requirements.
FRAs are used more frequently by banks, for applications such as hedging their interest rate exposures, which arise from mis-matches in their money market books. FRA�s are also used widely for speculative activities.


Characteristics of FRAs


Achieves the same purpose as a forward-to-forward agreement


Basically allows forward fixing of interest rates on money market transactions

Largest market in US dollars, pound sterling, euro, swiss francs, yen


BBA (British Bankers Association) terms and conditions have become the industry standard

FRA is a credit instrument (same conditions that would apply in the case of a non-performing loan) although the credit risk is limited to the compensation amount only

No initial or variation margins, no central clearing facility


Transaction can be closed at any stage by entering into a new and opposing FRA at a new price

An Example

A corporate with a $10 million floating rate exposure with rollovers to be fixed by reference to the 6-month USD LIBOR rate expects the short-term interest rates to increase. The next rollover date is due in 2 months. The corporate calls his banker and asks for a 2-8 USD FRA quote (6 month LIBOR 2 months hence). The bank quotes a rate 6.68 and 6.71 (see FRA table below). The customer locks the offered rate 6.71 (borrows at a higher rate).


If the 6-month LIBOR 2 months from now rises by 100 basis points to 7.71 the bank pays the corporate according to the BBA formula
(L-R) or (R-L) x D x A
[(B x 100) + (D x L)]

where: L = Settlement rate (LIBOR)
R = Contract reference rate
D = Days in the contract period
A = Notional principal amount
B = Day basis (360 or 365)

Note: Choose (L-R) or (R-L) so that the difference is positive
Therefore the bank would pay the corporate


(7.71 � 6.71) x 181 x $10 million = $48,401.53
[(360 x 100) + (181 x 7.71)]
If interest rates had fallen by 100 basis points the corporate would have to compensate the bank by an equivalent amount.

The result from this formula can also be obtained intuitively as follows:

The interest gain from entering the FRA is calculated as
1% x $10million x 181/360 = $50,277.78

The present value of $50,277.78 for a 6-month period discounted by the Settlement Rate (LIBOR) is:

$50,277.78 / {1+[7.71% x 181/360]} = $48,401.53

The (D x L) factor in the denominator of the BBA formula is the present value of the compensation at the settlement rate. The compensation amount in the above example is therefore discounted at 7.71 for the six-month period. This reflects the fact that the FRA payment is received at the beginning of the period (settlement date) and the party is therefore in a position to earn interest on it. The 6-month loan payment however is payable at the end of the period.

British Bankers Associations recommended terms
The BBA set up standards for FRA agreements, known as BBAFRA terms, to provide recommended terms and conditions for FRA contracts to provide guidance on market practice. Banks not dealing on BBA terms have to make it clear to the counterparty that the FRA is not governed by these terms.


Prices of FRAs are quoted the same way as money market rates, i.e. as an annualized percentage. FRAs are written as 3-6, 2.8, 4×10, 6vs9 etc. The first figure denotes the Settlement Date, the last figure the Maturity Date, and the difference between the two figures is the Contract Period.

FRAs are sometimes quoted as “offer-bid” rates, the same method of quoting followed by money market rates. The buyer of the FRA therefore gets the higher rate or the market maker�s offered rate since the buyer is a potential borrower. Likewise, the seller or depositor gets the lower rate or the bid rate.

The main Contract Periods traded are 3 months and 6 months although 12-month periods are gaining popularity. Broken date prices are also available though the spreads maybe wider and may take longer to obtain. Contract periods less than 3 months are difficult to obtain due to the nature of FRA trading (slim profit margins make it uneconomical).


The compensating amount reflects the difference between the actual / Settlement Rate for the period and the Contract Rate. The Settlement Rate, according to the BBA definition, is the rate calculated by taking the rates quoted by eight BBA Designated Banks as being in their view the offered rate at which deposits in the Contract Currency for such Contract Period are being quoted to prime banks in the London interbank market at 11.00 a.m. on the relevant Fixing Date for Settlement Date value. The two highest and the two lowest rates are eliminated and the remaining of the four rates are averaged and then rounded upwards to five decimal places.

In the event that the Settlement Rate is higher than the Contract Rate the borrower would receive payment from the seller. Conversely, the depositor would receive the compensating amount if the interest rates fall. Settlement of the compensating amount takes place at the beginning of the FRA. The first date of the Contract Period is defined as the Settlement Date. Euro FRAs rates are fixed two days ahead of the Settlement Date.

As the payment is an upfront payment the Compensating Amount is a discounted amount. The actual/discount rate used to calculate the Compensating Amount is taken as LIBOR or the offer rate of the money market quote. For market makers (usually banks) who expect to deposit at the offer rate and buyers of FRAs this method of discounting is not a problem. Sellers of the FRA will be disadvantaged if they place their deposits on the bid side of the quote and therefore will not be hedged at the Contract Rate. Their effective hedge will be lower by the spread between the quotes (usually 1/8%).

Hedging future interest rate exposure is the predominant use of a FRA. Banks hedge their money market mis-matches and corporates for future borrowings/deposits. Arbitrage between FRAs and short-term interest rate futures provide a good opportunity to banks. These short-term futures contracts provide a good source of hedging for FRA market makers.

Arbitrage between FRAs and forward-forward rates in the cash markets may be theoretically possible but rarely seen in practice. Speculation in FRAs is attractive, as there are no transaction fees involved. This type of activity is usually confined to banks.


There are many variations to the traditional FRAs and are gaining popularity. These include –

“Strip” FRAs or a combination of FRAs to lock a series of interest rates reset periods.

Forward Spread Agreements (FSAs) are essentially used to lock the interest rate differentials between two currencies. This type of transaction is entered between two parties who wish to hedge themselves against future changes in the LIBOR for two currencies one of which being the USD.

FRAs can be priced off forward to forward interest rates. These forward to forward rates can be obtained from the cash market yield curve or by the implied forward rates available from the interest rate futures market in the relevant currency.

Banks have recently started to quote FRA prices in the Indian currency. Forward rates can be constructed from securities of different maturities. FRAs in rupee can be synthetically created using the USD FRA in conjunction with rupee forwards in the foreign exchange markets or rupee interest rate swaps against MIBOR. However, forward rates in the foreign exchange markets are liquid upto 12 months only.

For example, suppose an Indian corporate is to issue a 6-month commercial paper. The current 3-month CP rates are 10.80 and the 6-month rates are 11.50. The corporate is of the view that the 6-month rates are high and is of the view that the rates should fall in the near term. The corporate could then sell a 3×6 FRA. If the rates do fall the corporate would receive the compensating amount from his bank therefore reducing his borrowing cost. Alternatively the corporate could issue a 3-month CP at 10.80%, lock in the 3×6 FRA rate, and issue another 3-month CP after 3 months (this strategy assumes the CP issuance costs involved are negligible). The Indian bank in turn could hedge his exposure in the forward markets by paying (borrowing) 6-month forward and receiving (lending) 3-month forward. Typical trading lot size would be 10 crores although 5 crores may be acceptable.


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