A forward rate agreement (FRA) is one of the most fundamental interest rate derivatives in fixed income markets. Whether you’re hedging a floating-rate loan, studying for the CFA exam, or building intuition for how derivative pricing works, understanding FRAs is essential. This guide covers everything you need to know — what an FRA is, how the notation works, how to price and value one, and how settlement is calculated. For the underlying yield curve theory connecting spot rates and forward rates, see our Spot Rates and Forward Rates guide.
What Is a Forward Rate Agreement?
A forward rate agreement (FRA) is an over-the-counter (OTC) derivative contract in which two parties agree on a fixed interest rate to be applied to a notional principal amount for a specified future period. FRAs are cash-settled — no actual borrowing or lending of the notional occurs.
The buyer (long position) of an FRA locks in a borrowing rate and benefits when interest rates rise above the agreed FRA rate. The seller (short position) locks in a lending rate and benefits when rates fall below the FRA rate. This makes FRAs a straightforward tool for hedging short-term interest rate exposure.
Corporations with floating-rate debt use FRAs to protect against rate increases. Banks use them to manage the interest rate risk in their lending and funding books. Portfolio managers use FRAs to express views on the direction of short-term rates without restructuring existing positions.
FRA Notation and Key Terms
FRAs use a standardized A×B notation where A is the number of months until settlement and B is the number of months until the end of the reference period. The difference (B − A) is the length of the borrowing period the FRA covers.
Trade Date → (3 months pass) → Settlement / Fixing Date (month 3) → (3-month reference period) → Maturity Date (month 6)
The FRA covers a 3-month borrowing period starting 3 months from now. Settlement occurs at the start of this period, not the end.
| FRA | Settlement Date | Reference Period | Borrowing Period |
|---|---|---|---|
| 1×4 | 1 month | Month 1 to month 4 | 3 months |
| 3×6 | 3 months | Month 3 to month 6 | 3 months |
| 6×9 | 6 months | Month 6 to month 9 | 3 months |
| 6×12 | 6 months | Month 6 to month 12 | 6 months |
Key terms:
- FRA rate (contract rate, K) — the fixed interest rate agreed upon at inception
- Reference rate (Rref) — the market benchmark rate observed at the fixing date (typically SOFR, EURIBOR, or SONIA since the LIBOR transition completed in 2023)
- Notional principal (N) — the face amount used to calculate the settlement payment (never exchanged)
- τ (tau) — the day count fraction for the reference period, calculated as days / 360 under the Actual/360 convention commonly used for FRAs
FRA settlement occurs at the start of the borrowing period (the settlement date), not at maturity. Because the payment is made “early,” it must be discounted — this is the single most important detail to remember when calculating FRA settlements.
How FRAs Work: The Settlement Mechanism
FRAs are cash-settled. At the settlement date, the reference rate is observed and compared to the contracted FRA rate. The party that is “out of the money” pays the difference to the other party, discounted to present value.
The numerator N × (Rref − K) × τ represents the interest difference that would be paid at the end of the reference period. The denominator (1 + Rref × τ) discounts this amount back to the settlement date because payment occurs at the beginning of the period. If the result is positive, the seller pays the buyer; if negative, the buyer pays the seller.
FRA Pricing: The Fair FRA Rate from Spot Rates
The fair FRA rate is the forward rate implied by the current spot curve. Under the no-arbitrage framework, the FRA rate must be the rate that makes the contract’s initial value zero — meaning neither party has an advantage at inception.
Given money market spot rates (Actual/360):
- 3-month spot rate (sA): 4.80% (A = 90 days)
- 6-month spot rate (sB): 5.10% (B = 180 days)
K = [(1 + 0.051 × 180/360) / (1 + 0.048 × 90/360) − 1] × (360 / 90)
K = [(1.0255) / (1.012) − 1] × 4 = [1.01334 − 1] × 4 = 0.01334 × 4 = 5.34%
The fair 3×6 FRA rate is 5.34%. At this rate, the contract has zero initial value — any other rate would create an arbitrage opportunity.
For a deeper explanation of how forward rates are derived from the spot curve, including bootstrapping and the no-arbitrage identity, see our complete guide on spot rates and forward rates.
FRA Valuation: Calculating the Value of an Existing FRA
After inception, market interest rates change and the FRA takes on a positive or negative value. To mark an existing FRA to market, you compare the original contracted rate (K) to the current market forward rate (Fnew) for the same period and discount the difference.
If forward rates have risen above the original FRA rate, the long (buyer) position has a positive value — they locked in a lower rate than the market now offers. Conversely, if forward rates have fallen, the buyer’s position is worth less than zero.
FRA Settlement Example
Contract terms:
- FRA: 3×6 (3-month rate starting in 3 months)
- Notional principal (N): $1,000,000
- FRA rate (K): 5.00%
- Day count: Actual/360
- Reference period: 90 days (τ = 90/360 = 0.25)
At settlement, the reference rate (Rref) is observed at 5.80%.
Step 1: Calculate the interest difference (undiscounted):
$1,000,000 × (0.058 − 0.050) × 0.25 = $1,000,000 × 0.008 × 0.25 = $2,000
Step 2: Discount to settlement date (payment occurs at the start of the period):
$2,000 / (1 + 0.058 × 0.25) = $2,000 / 1.0145 = $1,971.41
Result: The seller pays the buyer $1,971.41. The buyer locked in 5.00% but rates rose to 5.80%, so the buyer is compensated for the 80 basis point difference on $1,000,000 for 90 days, discounted to present value.
FRAs vs Interest Rate Futures
Both FRAs and interest rate futures allow market participants to hedge or speculate on short-term interest rate movements, but they differ in important structural ways:
Forward Rate Agreement (FRA)
- OTC — traded bilaterally, customizable terms
- Flexible notional, dates, and reference period
- Cash settled at the start of the period (discounted)
- Counterparty credit risk (collateral/clearing arrangements may vary)
- Not exchange-margined; bilateral margin arrangements may apply
- Single settlement at the fixing date
Interest Rate Futures
- Exchange-traded — standardized contract specifications
- Fixed contract sizes and quarterly expiration dates
- Daily mark-to-market with margin settlement
- Clearinghouse substantially reduces counterparty credit risk
- Initial and variation margin required daily
- Convexity bias: daily MTM means futures rates don’t equal FRA rates directly
The convexity bias between FRAs and futures is a practical consideration: because futures are marked to market daily while FRAs settle once, futures-implied rates must be adjusted (typically downward) to be comparable to FRA rates. This adjustment grows with maturity and rate volatility.
FRAs vs Interest Rate Swaps
FRAs and interest rate swaps are both OTC interest rate derivatives, but they serve different hedging horizons. An FRA covers a single future period — for example, the 3-month rate starting 3 months from now. An interest rate swap is a series of periodic exchanges over multiple periods, typically spanning several years.
In fact, a plain vanilla interest rate swap can be decomposed as a portfolio of consecutive FRAs, where each FRA corresponds to one swap payment period. Both instruments carry counterparty credit risk as OTC contracts. For short-term, single-period hedging, FRAs are the natural choice. For longer-term exposure spanning multiple periods, swaps provide a more efficient solution. For a comprehensive guide to swap mechanics and valuation, see our article on interest rate swaps.
How to Calculate Forward Rate Agreement Settlement
Follow these steps to calculate the settlement amount of any FRA:
- Identify the FRA terms: Read the A×B notation to determine the settlement date, reference period, notional (N), and contracted FRA rate (K)
- Determine the reference rate: Observe the market benchmark rate (e.g., SOFR) at the fixing date (Rref)
- Calculate the interest difference: N × (Rref − K) × τ, where τ = days/360
- Discount to settlement date: Divide by (1 + Rref × τ) since settlement occurs at the start of the reference period
A positive result means the buyer receives payment; a negative result means the buyer pays the seller. For step-by-step video lessons on FRA pricing and settlement, explore the Fixed Income Investing course.
Common Mistakes
These are the most frequent errors when working with forward rate agreements:
1. Confusing the FRA rate with the current spot rate. The FRA rate is a forward rate for a future period, not today’s borrowing rate. A 3×6 FRA rate reflects the implied 3-month rate starting 3 months from now — it is derived from the relationship between the 3-month and 6-month spot rates, not from either rate individually.
2. Forgetting to discount the settlement amount. This is the most common calculation error. Because settlement occurs at the start of the reference period (not the end), the payment must be present-valued by dividing by (1 + Rref × τ). Skipping this step overstates the settlement amount.
3. Using the wrong day count convention. FRAs in most markets use Actual/360. Applying 30/360 or Actual/365 will produce incorrect results. Always confirm the day count convention specified in the contract before calculating.
4. Confusing buyer and seller perspectives. The buyer (long) benefits when rates rise above the FRA rate — they locked in a lower borrowing cost. The seller (short) benefits when rates fall. Getting the sign wrong inverts the entire settlement.
5. Mixing compounding conventions between pricing and settlement. FRA pricing uses money market (simple interest) convention, while spot rates from bond markets may use annual or semi-annual compounding. Ensure all rates are converted to the same convention before plugging them into formulas.
Limitations of Forward Rate Agreements
FRAs are OTC derivatives that may carry counterparty credit risk. Unlike exchange-traded futures backed by a clearinghouse, FRA counterparty protection depends on the specific credit support arrangements (CSA collateral, bilateral netting, or voluntary central clearing) between the parties.
1. Liquidity constraints. FRAs are generally less liquid than standardized interest rate futures, resulting in wider bid-ask spreads — particularly for non-standard tenors or longer settlement dates. This can increase hedging costs for interest rate risk management.
2. Single-period coverage only. An FRA covers one future interest rate period. For multi-period hedging spanning quarters or years, interest rate swaps are more efficient than layering multiple FRAs.
3. Customization tradeoff. While custom terms (any notional, any dates) are an advantage, they also mean FRAs are harder to unwind or offset than standardized futures contracts with active secondary markets.
4. Reference rate transition. The global transition from LIBOR to alternative reference rates (SOFR, SONIA) and reformed benchmarks (EURIBOR) completed in 2023, changing FRA market conventions. Practitioners working with legacy contracts or transitioning portfolios should verify which reference rate applies. For broader context on how rate changes affect bond portfolios, see our guide on yield curve strategies.
Frequently Asked Questions
Disclaimer
This article is for educational and informational purposes only and does not constitute investment or financial advice. The examples use simplified assumptions (Actual/360 day count, no transaction costs) for clarity. Actual FRA terms, reference rates, and settlement conventions may vary by market and counterparty agreement. Always conduct your own analysis and consult a qualified financial professional before entering into derivative contracts.
