# Forward Rate agreements

Hi,

Confused with the 3 x 9 convention. If the FRA is expiring in 3 months then how come the underlying is starting after the 3 months have expired.

Also Why do we say that FRA expires after 3 months according to my example?

Because that’s the definition of an FRA: it’s essentially an agreement to enter into two loans (one long, one short, one fixed, one floating) starting on the day the FRA expires.

It’s an idea similar to that of a forward contract: the underlying is the sale/purchase of an asset, and that transaction occurs when the forward contract expires.

Because that’s when the settlement of the loans occurs: that’s when you pay or receive cash.

But when the FRA expires and the settlement has occurred then what happens to the underlying in the remaining 9 months according to 3 x 9. Because according to the forward contract the settlement occurs only at the end when asset is delivered or cash is exchanged, whichever and there is no asset remaining after that.

In an FRA you don’t enter into actual loans; that’s why I said that it’s essentially an agreement to enter into those loans.

When the FRA expires, you know the fixed rate and you know the floating rate, so you know the payoff. You could wait 6 months and make the payoff then, but the convention is to discount that payoff to today and make it today.

Can you please explain the entire process? Also why doe we have FRA i.e. its purpose?

Hmm… my understanding is FRA is simply a hedge tool. You use the payoff to compensate you for the interest rate moves unfavorably. You still pay the higher interest rate but the payoff in the FRA makes you “whole” sort of speak.

1. You enter into a 3 × 9 FRA as the fixed-rate payer: the notional is \$10 million and the fixed rate is 4.0%.
2. You wait 3 months. Maybe you go see a movie.
3. In 3 months the FRA expires, and the current 6-month floating rate is 3.8%. You pay the present value of 0.2% (= 4.0% − 3.8%) on \$10 million:

0.2% × \$10,000,000 × 6/12 / [1 + (3.8% × 6/12)] = \$9,813.54

Think of it as a 1-period swap. Maybe you have a floating-rate payment due and you’re concerned that interest rates will rise: you enter into an FRA as the fixed-rate payer to mitigate the risk.

Thank you S2000magician, that was very helpful.

My pleasure.

Right - the other way to think of the hedge is that if you have a pre-existing floating rate obligation you enter into an FRA to receive floating (i.e. match your liability cash flow) and pay a known fixed amount.

If I want to deposit money in future and make FRA in future, is that mean I’m short FRA?

but if I want to loan money in future and make FRA in future, is it mean I’m long FRA?

You’re long an FRA if you’re receiving the floating rate.

You’re short an FRA is you’re paying the floating rate.