Question

On 1st of January your CFO decides that 1 million euros will be needed at 1st of April for a time span of three months, so you will be looking for a loan and a way to hedge the interest risk. Current interest rates are 5.5% and they are expected to go down, while inflation is expected to stay at 1%. Forward rate agreements for your kind of loan are offering 5.0% and you are interested in securing this rate for your future loan so you enter this contract for the notional amount.

1) State how would the FRA be denominated

2) Calculate the outcome of the FRA, the expected interest cashflow, the effective cashflow and effective interest rate of the strategy, if at April 1st the interest rates have moved to:

a) 4.5%

b) 6.0%

3) Determine at what spot interest rate the FRA would expire worthless.

Deliverable: Word or Excel file showing the calculations, explanations and answers.

Answer 1

Forward rate agreements (FRA) are an over-the-counter contract between parties that determines the rate of interest, or the currency exchange rate, to be paid or received on an obligation beginning at a future start date. Parties who want to hedge their interest rate risk may enter into a Forward Rate Agreement if they see an exposure to interest rate in the coming months. FRAs are cash settled with the payment based on the net difference between the interest rate and the reference rate in the contract. The notional amount is not exchanged.

An FRA is basically a forward-starting loan, but without the exchange of the principal. The notional amount is simply used to calculate interest payment. By enabling market participants to trade today at an interest rate that will be effective at some point in the future, FRAs allow them to hedge their interest rate exposure on future engagements.

In this case, we need a loan of EUR 1 Mn in 3 months for another 3 months of time and we expect the interest rates to fall from current rate of 5.5%. As we’re getting FRA @ 5%, we can enter into this agreement with the part who are offering @ 5%.

Important terms defining the FRA are as per below:

contract rate (or FRA rate)	The interest rate the two contracting parties negotiate on trade date. This rate will be compared to the settlement rate when calculating the settlement amount. It starts on the settlement date and ends on maturity date.
contract period	The time between the settlement date and maturity date of the notional loan. This period is 3 months in this case.
currency	The currency in which the FRA's notional amount is denominated. In this case it’s EURO.
fixing date	This is the date on which the reference rate is determined, that is, the rate to which the FRA rate is compared.
FRA buyer	By convention, the buyer of an FRA is the contracting party that borrows at the FRA rate (contract rate).
FRA seller	By convention, the buyer of an FRA is the contracting party that lends at the FRA rate (contract rate).
maturity date	The date on which the notional loan is deemed to expire. It’s 1st July.
notional amount	This is the notional sum for which the interest rate will be guaranteed and on which all interest calculations will be based. It’s EURO 1 Mn.
reference rate	The interest rate index the FRA rate will be compared against in order to determine the settlement amount. This will generally be an IBOR-type rate index with the same duration as the FRA's contract period. (for example 3-month EURIBOR for an FRA in euros with a 3-month contract period).
settlement amount	The amount calculated as the difference between the FRA rate and the reference rate as a percentage of the notional sum, paid by one party to the other on the settlement date. The settlement amount is calculated after the fixing date, for payment on the settlement date.
settlement date	The date on which the notional loan period (the contract period) begins and on which the settlement amount is being paid.
spot date	The date on which the FRA. Usually two business days after the trade date.
trade date	The date on which the FRA is negotiated between the two counterparties. It’s 1st Jan.
waiting period	The period comprised between the value date and the settlement date. Its 3 months.

Here, the FRA will be denominated as Notional amount of EUR 1 Mn, contract period will be 3 months. Contract rate will be 5% and the reference rate will be determined on 1^st April.          

2) a. If the rates have moved to 4.5% but as per FRA we locked in a rate of 5%, then the buyer of the FRA is at a loss and we need to pay the difference of 0.5% to the Lender. Effectively, our interest rate will be 5% (Borrowed at spot of 4.5% and paid 0.5% to the lender).

Interest Differential amount = [Settlement rate- FRA rate] * [contract period/12] * Notional

                                             = EUR -0.5%*3/12*1,000,000

                                             = EUR -1,250

Settlement Amount = Interest Differential/[ 1 + Settlement rate * contract period/]

                                = EUR -1,250/1.01125

                                = EUR -1,236.09

b. If the rates have moved to 5.5% but as per FRA we locked in a rate of 5%, then the buyer of the FRA is at a profit and we will receive the difference of 0.5% from the Lender. Effectively, our interest rate will be 5% (Borrowed at spot of 5.5% and received 0.5% from the lender).

Interest Differential amount = [Settlement rate- FRA rate] * [contract period/12] * Notional

                                             = EUR -0.5%*3/12*1,000,000

                                             = EUR 1,250

Settlement Amount = Interest Differential/[ 1 + Settlement rate * contract period/]

                                = EUR 1,250/1.01375

                                = EUR 1,233.046

3. At spot rate of 5%, the FRA would expire worthless as there would be 0 difference between the spot rate on 1^st April and the FRA rate on 1^st Jan.