Definition of Forward Rate Agreement

Applying "Forward Rate Agreement" to Securities Exams:

The terminology used might appear as a ‘3 x 6 FRAÕ meaning an agreement to pay/receive a fixed rate of interest starting in 3 months’ time and ending in 6 months’ time (therefore for a 3 month period).

• A company is going to receive $1m from the sale of an asset in 1 month’s time and will not need the cash until 6 months later. It decides it will deposit the money in a bank account to earn interest for 6 months when it receives the cash. The CFO is concerned that interest rates might fall and wants to lock in to a rate now.
• What should he do? If he buys a FRA he will make money out of rising rates. If he sells a FRA he will make money out of falling rates. To protect the interest rate on a deposit he therefore wants to sell a FRA, generating profits if rates fall. This will offset the lower rate on the deposit. Here he would want to sell a 1 x 7 FRA.
• A bank quotes a 4.5% 1 x 7 FRA; the treasurer agrees to sell and in 1 month’s time LIBOR has risen to 5%.
• Did the CFO generate a profit or loss by entering the FRA? He sold at 4.5%; but the interest rate is now 5% so the contract has made a loss. But he would now get a high rate on the deposit.
• But how much of a loss was made on the FRA?

Step 1
Calculate the difference in interest rates. In this example the company receives 4.5% and pays 5.0%. The annual difference is a 0.5% loss.

Step 2
Pro-rate the difference for the length of the contract -0.005 x 180/360 = -0.0025

Step 3
Apply the pro-rated difference in interest rates to the notional value of the contract. -0.0025 x $1,000,000 = -$2,500

Step 4
Discount the cash flow back to the expiration date. The payoff occurs at the expiration date therefore need to be discounted at LIBOR for six months. -$2,500 / 1.025 = $2,439

 

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