Forward Rate Agreement

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Forward Rate Agreements, or FRAs, are a way for a company to lock in an interest rate today, for money the company intends to lend or borrow in the future.

FRAs are cash-settled forward contract on interest rates. This means that no loan is actually extended, even though a notional principal amount mentioned in the contract. Instead, the borrower (buyer) and the lender (seller) agree to pay each other the interest difference between the agreed-upon rate (the "Forward Rate") and the actual interest rate on the future date (the "Floating Rate"). The cash settlement occurs on the day the loan is set to begin.

Many banks and large corporations will use FRAs to hedge future interest rate exposure. The buyer hedges against the risk of rising interest rates, while the seller hedges against the risk of falling interest rates. Other parties that use Forward Rate Agreements are speculators purely looking to make bets on future directional changes in interest rates.

An example would help illustrate the point. Suppose the current month is February. Widget Co. needs $5,000,000 in April which it can repay back in May. In order to hedge against the risk that interest rates may be higher in April than it is in February, the company enters into an FRA with Bank Z at 6% FRA rate. In this case it would be a 2X3 FRA, meaning a 1 month loan to begin in 2 months, with a notional principal of $5,000,000. In April, if the interest rate rises to 8%, Bank Z would pay Widget Co the increased interest arising from the higher rate. If on the other hand interest rate falls to 4%, Widget Co would pay Bank Z.

FRAs trade over the counter (OTC), and because they are not exchange traded, both the notional amount of the loan and the FRA rate can be negotiated and customized. Also, since the contract is cash settled, no loan is actually given or received, but rather the contracts are settled on the first day of the underlying loan.

FRA Terminology

The fixed rate, also called the FRA rate, is negotiated and agreed upon by both parties before the contract is entered into. The floating rate, also known as the reference rate, is an interest rate that will fluctuate between when the contract is agreed upon, and when the loan is set to begin. The two most common floating rates used in FRAs are LIBOR and Euribor.

FRAs are quoted in the format AxB, with (A) representing the number of months until the loan is set to begin, and (B) representing the number of months until the loan ends. To find the length of the loan, subtract A from B. For example, 1x4 quote would mean a 3 month loan, set to begin 1 month in the future. Common formats for these quotes include 1x4, 1x7, 3x6, 3x9, 6x9 and 6x12.

How do Forward Rate Agreements Work?

The mechanics and uses to using FRAs are best shown through an example. Throughout this example 3 months is equated to 90 days.

Mechanics of a FRA

Consider Company Z on March 1, 2009, which due to unforeseen circumstances must now find $10 million for an expenditure to occur on June 1, 2009. Company Z expects to generate revenue, and the company expects to be able to repay this amount on September 1, 2009. Company Z has a number of ways to meet this expenditure; in this example we only compare a traditional loan to an FRA.

Let's assume Company Z can normally borrow funds for 3 months from its local bank at a rate of 3 month Libor plus 100 basis points (bps). If the company takes the first alternative, the effective interest rate it would be able to borrow at would remain unknown until June 1, when it borrows the actual $10 million at 3 month LIBOR plus 100 bps. Note that this represents a variable interest rate, as the interest rate in 3 months remain unknown until the actual day arrives. What if the company wishes to know on March 1, 2009 the interest they must pay on the loan, which will not occur for another 3 months?

Company Z can also get a quote from a FRA dealer (normally a bank). In this example, the company needs a 3x6 FRA quote (with 3x6 meaning a 3 month loan, to begin in 3 months). Let's assume the FRA dealer offers a quote of 7.0%. This means if the 3 month Libor on June 1 is lower than 7.0%, the FRA dealer will earn the difference between 7.0% and the actual interest rate. Intuitively this makes sense, as the FRA dealer is earning 7.0% on this loan, but it can borrow at the lower 3 month LIBOR rate. However, if on June 1 the rate is higher than 7.0%, it will lose the difference.

If Company Z accepts the FRA rate of 7.0% on March 1, then 3 months later (June 1), it will settle in cash this difference between the previously agreed upon 7.0% and 3 month LIBOR on June 1 2009. If the 3 month LIBOR on June 1 is lower than 7.0%, the company must pay the FRA dealer. However, if it is higher, the company receives payment from the FRA dealer. Since the company is effectively borrowing at a lower interest rate than otherwise possible if the 3 month LIBOR is higher than 7.0%, and as such receives payment. To calculate the amount of the payment, refer to the formula below.

This payment is from the borrower's perspective. For positive quantities, the borrower pays the FRA dealer; for negative amounts, the borrower receives payment from the FRA dealer. The basis refers to the day count applicable for money market transactions. For U.S. Dollar (USD) and Euro (EUR), it is 360' for British Pound (GBP) it is 365.
This payment is from the borrower's perspective. For positive quantities, the borrower pays the FRA dealer; for negative amounts, the borrower receives payment from the FRA dealer. The basis refers to the day count applicable for money market transactions. For U.S. Dollar (USD) and Euro (EUR), it is 360' for British Pound (GBP) it is 365.

How FRAs lock in Interest Rates

It may seem confusing how giving or receiving cash payment helps the company lock in an interest rate. To understand the compensation payment in context, this example will be extended.

On June 1, only 3 possibilities can occur:

  1. the 3 month LIBOR is exactly 7.0%, no settlement is needed,
  2. the 3 month LIBOR is higher than 7.0%, Company Z receives payment,
  3. the 3 month LIBOR is lower than 7.0%, Company Z makes payment.

If the 3 month LIBOR on June 1 increased to 7.5% for example, then the FRA dealer must make payment to Company Z. Continuing with this example, the FRA dealer will pay Company Z $10 million*{ [ (7.0-7.5%)*(90/360) ] / [1+ (7.5%)*(90/360) ] }, which amounts to $12,269.94. If the 3 month LIBOR fell to 6.5%, the company would make an equal the payment to the FRA dealer. But how does this help Company Z achieve the previously agreed upon 7.0% rate?

If the 3 month LIBOR increased to 7.5%, then Company Z receives payment of $12,269.94. It then goes to its local bank (from the start of the example), and borrows $10 million less $12,269.94, or $9,987,730.06. Assuming its local bank's markup rate has not changed, it would need to repay $9,987,730.06 * [1+ ((7.5%+ 100 bps) * 90/360) ], or $10,199,969.32. This implies a quarterly rate of interest of 2.0% ($10,199,969.32/$10,000,000 -1), which annualized comes out to exactly 8.0%. This 8.0% rate is precisely the 7.0% locked in rate, plus the 100 bps markup rate.

If the 3 month LIBOR decreased to 6.5%, Company Z makes payment of $12,269.94 to the FRA dealer. It would again go to its local bank, but borrow $10 million plus $12,269.94, or $10,012,269.94. In 3 months time, it would need to repay $10,012,269.94 * [1+ ((6.5%+ 100 bps) * 90/360) ], or $10,200,000. This implies a quarterly rate of interest of 2.0%, which annualized comes out to 8.0%. Once again, the variable 3 month LIBOR has been replaced by the previously agreed upon FRA rate of 7.0%. As evidenced by this example, Company Z, as of March 1, knows its cost of borrowing $10 million, and this amount is independent of fluctuations in the 3 month LIBOR. When the 3 month LIBOR increases, it must borrow at a higher rate, but receives cash compensation from the FRA dealer. If the 3 month LIBOR decreases, it benefits from borrowing at a lower rate, but must pay the FRA dealer compensation.

Valuing a Forward Rate Agreement

A 6 X 12 FRA is priced at today's implied six-month forward, six-month interest rate (6R12). This rate can be calculated using the six-month (0R6) and one-year (0R12) interest rates by solving the following equation.

(1 + 0R6 * 0.5) * (1 + 6R12 * 0.5) = (1 + 0R12 *1)

The price of FRAs with different maturities can be calculated by setting up similar equations. For example, the price of a 3x6 FRA can be derived if 0R3 and 0R6 are known, a 3x12 can be priced if 0R3 and 0R12 are know etc.

To value an existing FRA one needs:

  • Notional principal P
  • Contract rate C
  • Forward period t1 to t2
  • Spot or zero coupon interest rates with maturities t1 and t2 (denoted 0R1 and 0R2, respectively).

Risks of Forward Rate Agreements

Because FRAs are settled in cash and no loan is actually extended, only the compensation amount is ever at risk. In other words, the most either party in a Forward Rate Agreement will lose is the amount that must be cash settled, and not the entire notional amount of the loan. Furthermore, two conditions must apply before a party faces losses;

  1. Interest rates move in favor of the party, entitling it to compensation by the counterparty, and
  2. The counterparty defaults and is unable to pay the compensation amount.
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