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# Forward Rate Agreements

Forward Rate Agreements - What are they?

Forward rate agreements (FRAs) are contracts for difference. They are traded in the over-the-counter (bilateral or non-exchange) market. They allow the two parties involved to hedge or speculate on interest rates in the future. Perhaps the easiest way to understand a FRA is to break it down into a loan and deposit. Let’s try.

Suppose you borrow \$10,000,000 for 182 days at a rate of 4% and then you lend the \$10,000,000 for 91 days at 3%.

In 91 days time your 3% loan will mature. You now have a further 91 days to re-lend the money. What interest rate must you obtain on this second loan in order to have enough capital to repay your original 6 month borrowing?

Amount:          \$10,000,000.00

Rate:                 4%

Days:                182

Interest:            \$202,222.22

Repayment:     \$10,202,222.22

Amount:            \$10,000,000.00

Rate:                  3%

Days:                 91

Interest:             \$75,833.33

Repayment:     \$10,075,833.33

The interest amount you must earn for the second 91 day period is (\$10,202,222.22 -\$10,075,833.33) = \$126,388.89

How much capital is at your disposal? \$10,075,833.33

So the rate you need to earn is:

126,388.89 / 10,075,833.33 x 360 / 91 =  4.96%

In other words the forward rate is 4.96%

When the short rate is lower than the long rate (a positive sloping yield curve) the forward rate is higher than spot interest rate. For a negative sloping yield curve the forward rate is lower than the spot rate.

What’s the connection with FRAs?

Banks don’t lend and borrow cash when trading forward rates, (too much credit and capital would be required). They just enter a deal based on the forward rate itself. Here’s how it works:

A dealer quotes a 3 x 6 FRA at 4.94 - 4.98

(3 x 6 refers to a three month rate starting in three months time)

A customer wishing to protect against rising interest rates enters into the FRA with the dealer at 4.98%. (Note the customer is getting the worst rate because the dealer dictates the terms of the trade).

What happens next?

The trade ticket is processed and the bank and customer confirm the deal. There is no exchange of money at this point.

We now wait three months in order to see where three month Libor “fixes”. It could be higher, the same as or lower than the rate on the trade (4.98%).

Let’s see what happens in each case.

Rate                 FRA                 Customer gain/loss

5.08%              4.98%              +0.10%

4.98%              4.98%               0.00%

4.88%              4.98%              -0.10%

When 3 month Libor fixes above 4.98% the customer gains and the dealer loses, when Libor fixes below 4.98% the customer loses and the dealer gains.

So just how could the FRA be of use?

For this customer an FRA can hedge against rising Libor rates. The sort of risk associated with variable rate loans. This is just one use. Money market dealers also use FRAs. They help them lock-in forward borrowing and lending rates and interest payments associated with Libor re-fixings. An additional attraction is that FRAs are bilateral trades and specific forward periods can be matched precisely.

Discounted settlement

One unusual feature of FRAs is their settlement. FRAs settle “up-front” that is on the date of the Libor fixing. This means the payment is discount. Let’s see this.

Take the case where Libor fixes at 5.08%. The customer profits by 0.10%. On a \$10,000,000 trade that is:

\$10,000,000 x 0.10% x 91 / 360 = \$2,527.77

This sum is discounted at the Libor rate of 5.08%

\$2,527.77 x 1 / (1 + 0.0508 x 91 / 360) = \$2,495.72 (the sum received by the customer)

Is there anything else?

Yes. You can calculate forward interest rates for any period in the future. Now that’s a useful piece of information. It gives you an unbiased view of where interest rates will be in the future. It’s useful not only for traders but also for anyone involved in the planning process.

One last point

Over-the-counter trades incur credit risk on the counterparty (the mark-to-market value and any potential future exposure). FRAs are no exception. Before dealing a credit assessment of the counterparty and a dealing limit are mandatory.