# Forward rate agreement: A hedging technique for interest rate risks

Published: April 26, 2017 3:53 AM

## Uncertainty regarding future rates of interest is a matter of concern to both potential borrowers as well as lenders.

Uncertainty regarding future rates of interest is a matter of concern to both potential borrowers as well as lenders. The former would be worried about the spectre of rising rates, while the latter would be concerned with the possibility of a rate decline. Consequently, both kinds of traders may wish to hedge the risk regarding future rates of interest. One such hedging tool is a forward rate agreement (FRA).

By using such a derivative one can lock in a rate of interest for a transaction scheduled for a future date. Forward rate agreements are cash settled. That is, on a specified future date the profit for one party, or equivalently, the loss for the other party would be computed.

A forward rate agreement is denoted as A x B, for instance 3 x 9. The first number denotes the time of commencement of the loan, while the difference in the two numbers represents the maturity of the loan. In this case, the rate is for a six-month loan, scheduled to commence after three months.

The rate of interest for a forward rate agreement is termed as the contract rate. The party who agrees to pay this rate is known as the buyer of the FRA or the long, while the counterparty is known as the seller of the FRA or the short. If the actual rate of interest after A months is higher than the contract rate, the long will receive a payment from the short. And, if the rate were to be lower, the long would have to make a payment to the short.

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Every FRA has a specified principal amount that is termed as the notional principal. The implication is that this amount is specified purely to facilitate the computation of the payment from one counter-party to another, and that neither party need borrow/lend this amount. The market rate of interest against which the contract rate is compared is termed as the reference rate, which is usually the London Interbank Offered Rate (LIBOR).

From a speculative standpoint, traders who are bullish about interest rates would buy FRAs, for they would receive a cash flow if rates were to rise, while traders who are bearish about rates would sell FRAs.

For instance, assume that a 3 x 9 FRA has a contract rate of 6% per annum, and assume that the day-count convention is 30/360. Let the notional principal be \$5 million. If, after three months, the LIBOR were to be 7.50%, the short would need to make a payment of 5,000,000 x (0.075-0.06) x (180/360) = \$37,500 to the long.

This payment would need to be made nine months from now. In practice, the present value of this amount would be computed and paid three months from now. That is, the amount of \$37,500 would be discounted using simple interest based on the prevailing LIBOR after three months, which we have assumed is 7.50%. Since the reference rate (LIBOR) is greater than the contract rate, the short will pay \$36,145 to the long.

If we are given money market interest rates, we can derive upper and lower bounds for the contract rate. For instance, assume the 3-month London Interbank Bid Rate (LIBID) is 2% while the 9-month LIBID is 3%. The 3-month LIBOR is 2.50% while the 9-month LIBOR is 3.8% per annum. The trader can borrow at the 3-month LIBID; go long in a FRA; and invest the borrowed amount at the 9-month LIBOR. This activity should obviously be profitable from his standpoint and consequently we can derive an upper bound for the contract rate.

The writer, Sunil K Parameswaran is an author and a visiting faculty at various business schools including the IIMs

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