Forward rate agreements (FRAs): settlement and uses

What is a forward rate agreement?

A forward rate agreement (FRA) is an over-the-counter contract in which two counterparties agree to apply a specific interest rate to a future period. The underlying is a hypothetical deposit of a notional amount at a market reference rate (MRR) , such as the Secured Overnight Financing Rate (SOFR) or Euribor, that will set at the start of that period.

A “3×6” FRA (read “three by six”) covers the three-month period that starts in three months and ends in six. Forward-rate labels count differently: the same period is the 3m3m rate, which starts in three months and runs for three months.

The FRA buyer is the long position. It is the fixed-rate payer : it pays interest at the agreed FRA rate and receives interest at the reference rate. The seller does the reverse. The notional is never exchanged; it only scales the interest.

Forward rate agreementfixes a rate for a future period on a notional; only the net is paid

• Long (FRA buyer) Memorize fixed-rate payer, floating-rate receiver
  • Gains when the reference rate sets above the FRA rate
  • Hedges a future borrowing or floating-rate liability
• Short (FRA seller) Memorize fixed-rate receiver, floating-rate payer
  • Gains when the reference rate sets below the FRA rate
  • Hedges a future deposit or floating-rate investment

What is the FRA rate?

The FRA rate is set so that the contract has zero value at the start, like any forward. The no-arbitrage rate is the implied forward rate for that period, the breakeven rate from the previous lesson.

$$FRA\ rate = IFR_{A,B-A}$$

How is an FRA settled?

At the start of the interest period (t = A) the reference rate sets, and the FRA is cash settled. Interest on the deposit would be due at the end of the period (t = B), so the FRA first computes the net payment at the end of the period.

$$Net = (MRR - FRA\ rate) \times N \times \frac{D}{360}$$

A positive net is paid to the buyer; a negative net is paid by the buyer. Because that interest is not due for another D days, the FRA uses cash settlement at the start of the period : the net is discounted back to t = A at the reference rate that has just set.

$$Settlement = \frac{Net}{1 + MRR \times D/360}$$

Three datest = 0, t = A, t = B

• t = 0, contract Memorize FRA rate fixed at the implied forward rate; value is zero
• t = A (3 months), reference rate sets Memorize cash settlement paid, discounted at MRR
• t = B (6 months), period ends Use it the interest the net payment stands for is due

Slide the reference rate above and below 3.40%. Above it the buyer is paid; below it the buyer pays. The amount is the rate gap on the notional for the period, brought back to the start.

Exam tip Two steps every time: net payment with the day fraction, then divide by (1 + MRR × days/360).

How do I pick the right position?

Match the exposure, not the market view. A party that loses when rates rise buys the FRA; a party that loses when rates fall sells it. This is hedging rate-sensitive liabilities (and assets) with a forward rate.

How does an FRA relate to a forward and a swap?

An FRA is a forward on an interest rate. It is also a one-period interest rate swap: fixed versus floating, net settlement, notional never exchanged. A swap is a strip of such single-period exchanges. FRAs are used almost exclusively by banks and other intermediaries to manage rate-sensitive assets and liabilities. Issuers and investors more often use swaps.

Go deeper Why discount at the reference rate?

The net payment stands for interest due at the end of the period, but the FRA is paid at the start. To bring it back one period you use the rate at which money can be borrowed or lent for that period, which is the reference rate that has just set. The FRA rate was relevant only for the original fixed leg.

Go deeper Day count conventions in one line

Many money market rates use actual days over 360 (some currencies use 365). A 90-day period is 90/360 = 0.25 of a year. Use the day fraction the question gives.