Forward Rate Agreement
A Forward Rate Agreement (FRA) is an over-the-counter interest rate derivative in which two parties agree today on a fixed interest rate to be applied to a notional principal amount for a specified future period, with a cash settlement at the start of the reference period based on the difference between the contracted rate and the prevailing market reference rate. FRAs allow borrowers and lenders to lock in an interest rate for a future period without exchanging the underlying principal.
Key takeaways
- An FRA is quoted as 'X × Y' where X is the number of months until the contract period starts and Y is the number of months until the contract period ends; a '3×6 FRA' hedges a three-month borrowing or lending rate starting in three months.
- At settlement date (start of the reference period), the FRA pays: Notional × (Reference Rate − FRA Rate) × (Days/360) / [1 + Reference Rate × (Days/360)], with the discounting adjustment reflecting that settlement occurs at the start of the reference period rather than at the end.
- FRAs are the OTC equivalent of short-term interest rate futures (such as SOFR futures or Eurodollar futures) and are priced consistently with futures through no-arbitrage relationships, though they differ in that futures are exchange-traded and margined daily while FRAs settle net in cash.
- The primary users of FRAs are banks managing their interest rate gap (mismatch between fixed and floating assets and liabilities), corporations locking in funding costs, and derivatives dealers hedging interest rate risks in their swap and options books.
- Following the LIBOR transition, FRAs have progressively shifted from LIBOR-based reference rates to overnight risk-free rate (RFR) compounded-in-arrears settings (SOFR, SONIA, €STR), though liquidity in term RFR-based FRAs has been building gradually.
Explanation
The Forward Rate Agreement is the fundamental building block of the interest rate derivatives market, providing the simplest mechanism for isolating and transferring interest rate risk for a single future period. Unlike an interest rate swap—which involves a series of interest rate exchanges over multiple periods—an FRA is a single-period contract, making it conceptually equivalent to a single 'leg' of a swap. Indeed, an interest rate swap can be decomposed into a series of FRAs, one for each reset period of the floating leg.
The pricing of FRAs relies on the same no-arbitrage framework that governs all interest rate derivatives. The fair FRA rate for a contract period from T₁ to T₂ must equal the forward interest rate implied by the current yield curve for that period. Using simple interest rates:
FRA Rate = [(1 + r₂ × T₂) / (1 + r₁ × T₁) − 1] / (T₂ − T₁)
where r₁ and r₂ are the spot interest rates (on an act/360 basis) for maturities T₁ and T₂ respectively. This relationship ensures that any deviation of the market FRA rate from the implied forward rate creates a riskless arbitrage opportunity for participants with access to the money market.
The settlement mechanics of an FRA are distinctive. Unlike many derivatives that settle at maturity, FRAs settle at the beginning of the reference period (T₁) rather than at the end (T₂). This reflects the fact that the FRA is intended to hedge a borrowing or investment that begins at T₁; paying or receiving at T₁ is economically equivalent to receiving the full interest flow at T₂ after discounting, but requires a present value adjustment. The settlement formula explicitly includes this discounting: the difference between the reference rate and the FRA rate, applied to the notional and the day count fraction, is discounted back from T₂ to T₁ using the realized reference rate.
In the hedging context, an FRA serves a precise and practical purpose. A corporate treasurer who knows that their company will need to borrow $50 million for three months starting in three months (a '3×6' period) is exposed to the risk that the benchmark borrowing rate will rise between now and the start of the borrowing period. By buying a 3×6 FRA—agreeing to pay a fixed FRA rate and receive the then-prevailing reference rate—the treasurer locks in the effective borrowing cost at the current forward rate. If market rates rise, the FRA pays the treasurer the excess, offsetting the higher borrowing cost; if rates fall, the treasurer pays the FRA counterparty the shortfall, but their borrowing cost also falls by the same amount, leaving the net cost unchanged.
The interest rate swap market is closely related to the FRA market. A vanilla interest rate swap can be priced as a portfolio of FRAs, one for each semi-annual or quarterly period of the swap's life. The par swap rate—the fixed rate at which the swap's present value is zero—can be computed by finding the rate that equates the present value of fixed cash flows (discounted at swap discount factors) to the present value of the floating leg (represented by the strip of forward rates embedded in the swap discount curve). Swap dealers use the FRA market as one of their primary hedging tools for managing the residual risks in their swap books.
Formula
FRA Settlement = N × (R_ref − R_FRA) × (Days/360) / [1 + R_ref × (Days/360)]
Example
A corporate treasurer expects to borrow $10 million for three months starting in three months' time. The current 3-month SOFR rate is 5.25%, and the 6-month SOFR rate is 5.40%. The implied 3×6 SOFR forward rate is approximately: [(1 + 0.054 × 0.5) / (1 + 0.0525 × 0.25) − 1] / 0.25 ≈ 5.55%. The treasurer buys a 3×6 FRA on $10 million notional at a fixed rate of 5.55%. Three months later, when the FRA settles, the 3-month SOFR fixing has risen to 6.00%. The FRA settlement amount is: $10M × (0.06 − 0.0555) × (90/360) / [1 + 0.06 × (90/360)] = $10M × 0.00450 × 0.25 / 1.015 ≈ $11,084. The treasurer receives $11,084 from the FRA counterparty, which offsets the approximately $11,250 additional interest cost on the bank loan from the rate increase. The net borrowing cost is effectively locked in at approximately 5.55% regardless of the actual prevailing rate.
Related terms
Arbitrage Basis Call Option Cash Settlement Current Yield Gamma Hedging Interest Rate Interest Rate Swap Margin Open Interest Present Value