In this post we’ll cover what is a Forward Rate Agreement (FRA).

An FRA is an interest rate derivative. This means its price is determined by the variations in interest rates.

But there’s more to it:

## What is a Forward Rate Agreement?

**A Forward Rate Agreement is a contract between two parties that establishes an interest rate for a future date.**

These two parties—* buyer *and

*—agree to exchange the interest payment on a certain notional amount (amount used to calculate the payment made).*

**seller**The buyer agrees to pay a ** fixed **rate to the seller, also called the FRA rate.

The seller agrees to pay a * floating* rate, also called the reference rate. This is usually the rate at which major banks lend to one another—the LIBOR. It changes every day.

An FRA can be used as a * hedging *instrument for both deposits and loans, as it allows you to establish,

*today*, a future interest rate.

You can also use them as a * speculative *instrument to bet on the future variation of interest rates.

## How Forward Rate Agreements Work

The FRA is a *single *exchange of cash flows (unlike Interest Rate Swaps).

And no payment will take place until the future floating rate is known.

Instead, FRAs are ** cash-settled**.

This means in practice, one counterparty makes one payment to the other. One single cash flow from A to B to settle the difference between the fixed interest rate and the floating rate.

Both rates are applied to a specified notional amount, but that amount itself is not exchanged.

**What is exchanged is a cash amount based on the contract’s notional value and the difference between rates.**

The long position pays the fixed rate, and receives the floating rate. This means they guarantee the rate they need to pay on a future loan.

As the buyer, you will still **pay **the future floating rate on your future loan. However, since you’ll also **receive **that *same *rate from your FRA counterparty, it *offsets *the total amount you need to pay. What’s left to pay? The fixed rate you always wanted.

Meanwhile, the short position pays the floating rate, and receives the fixed rate. This means they guarantee the rate they’re going to receive on a deposit.

*How?*

As a depositor, you’ll receive the future floating rate on your future deposit.

But if you’re concerned interest rates will go down in the future. What can you do?

Sell a Forward Rate Agreement, where you’ll pay that floating rate to the buyer of your FRA. So, net 0. What do you receive in exchange? The fixed rate you always wanted.

## What is the Advantage of a Forward Rate Agreement?

There are advantages to both sides—buyer and seller.

We can sum them up to this:

Buyer | Seller | |

Goal | Hedges against a rise in interest rates | Protection against a fall in interest rates |

Interest Rate | Pays a fixed interest rate | Receives a fixed interest rate |

Result | Fixes the maximum cost for a loan | Secures the minimum rate they’ll get for a deposit |

## Equation for a Forward Rate Agreement

So, how do you calculate an FRA? What’s the formula?

Well, if you want to calculate its payoff, you can use this formula for the long position:

And this one for the short position:

Where ** N** is the notional amount of the contract,

*is the fluctuating rate, and*

**r***is the fixed rate.*

**F*** n* transforms the yearly rate into the effective rate. For example, if the FRA has a duration of 6 months, you need to divide the yearly rate by 2 to reflect that. In this example, n would be 2.

Put simply, **the payoff of a Forward Rate Agreement is the notional value multiplied by the difference in interest rates**.

Now, how do you calculate the *value *of an FRA?

The intrinsic value (not market value) of any asset is the present value of all future cash flow it is expected to generate.

To get the value of an FRA, simply discount its payoff to the present.

## Forward Rate Agreement Example

Suppose that *3 months from now (T1)* you know your firm will need to borrow $5M for 6 months.

The problem? You’re concerned interest rates might go up between today and time T1.

To hedge against the possibility of a rate hike, you guys buy an FRA to fix the rate at 4%.

3 months pass by and you were right. Nice call! Interest rates increased and are now 5%.

The firm takes out a loan at 5%. But that’s ok. Since they are the *buyer *of the FRA contract, they receive that rate from the seller. In return, they pay the seller the 4% fixed rate.

Plug this into the formula and you’ll find the FRA payment is:

$25,000 is the amount the seller will pay the buyer (your firm) to offset the increase in interest rates, therefore fixing the rate.