Settlement is discounted to present value at the fixing date.
Understanding the Inputs
Notional Amount
The principal amount on which the interest rate differential is calculated. This is not exchanged between parties—only the settlement payment based on interest rate differences is paid. Enter the notional value in your currency.
Agreed Forward Rate (%)
The forward interest rate agreed upon when entering the FRA contract. This is the rate that the parties expect at the start of the contract period. Enter as an annual percentage (e.g., 4.5 for 4.5%).
Market Rate at Settlement (%)
The actual reference interest rate prevailing in the market when the FRA contract period begins. This is compared to the agreed rate to determine the settlement payment. Enter as an annual percentage.
Months from Today (start/end)
The start and end months define the contract period for which the interest rate is being forward-priced. For example, a "6x9 FRA" starts in 6 months and covers the period until month 9. Enter the number of months from today.
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A **Forward Rate Agreement (FRA)** is an Over-the-Counter (OTC) contract between two parties that determines the interest rate to be applied to a notional principal amount for a specific period of time in the future. It is a commitment today regarding an interest rate that will only be used later.
FRA Notation (n x m)
FRAs are quoted using an "n x m" notation (read as "n by m") that defines the start and end of the forward period, measured in months from the settlement date (today):
n: The number of months until the forward contract begins (the fixing date).
m: The number of months until the forward contract expires.
The duration of the actual borrowing/lending period under the contract is $(m - n)$ months. For example, a **3 x 6 FRA** begins in 3 months and expires in 6 months, locking in a rate for a 3-month period that begins 3 months from now.
The Two Sides of the Contract
Buyer (Fixed Rate Payer): Enters the FRA to protect against rising interest rates. The buyer pays the agreed-upon fixed FRA rate.
Seller (Floating Rate Payer): Enters the FRA to protect against falling interest rates. The seller pays the variable market rate (the reference rate) at the fixing date.
Pricing the FRA: Deriving the Contract Rate
The contract rate (or FRA rate) is set at the origination of the contract such that the theoretical initial Net Present Value (NPV) of the agreement is zero. This rate is derived directly from the current **Yield Curve** (the relationship between interest rates and maturity).
The Forward Rate Formula (No Arbitrage)
The FRA rate is the implied forward rate between two zero-coupon bonds (or spot rates) on the yield curve. It ensures that an investor who invests for the short period ($n$ months) and then reinvests at the forward rate for the longer period ($m-n$ months) earns the same return as if they invested for the long period ($m$ months) today.
Where R long and R short are the spot rates for the longer and shorter time periods, respectively, and T represents time in years (or fraction of a year).
Settlement Mechanics and Payoff Formula
FRAs are typically settled in cash at the start of the forward contract period (at time $n$), not at the end of the period ($m$). This early settlement necessitates discounting the cash flows back from time $m$ to time $n$.
The Fixing Date and Reference Rate
On the **Fixing Date** ($n$), the actual **Reference Rate** (e.g., SOFR, LIBOR) is observed. The difference between this market rate and the contracted FRA rate determines the settlement amount.
The Settlement Payoff Formula
The settlement is calculated as the present value of the difference in interest payments, paid at time $n$:
Where R reference is the market rate at time n, R FRA is the fixed contract rate, and T period is the length of the contract period (m minus n).
If R reference > R FRA, the Buyer (fixed-rate payer) receives a payment from the Seller.
If R reference < R FRA, the Seller receives a payment from the Buyer.
Market Applications: Hedging and Speculation
FRAs are primarily used for hedging interest rate risk, but their structure also allows for simple speculation on the future direction of interest rates.
Hedging Future Borrowing Costs
A corporate treasurer who knows the firm will need to borrow money in three months for a period of three months (a 3 x 6 FRA) can purchase an FRA today to lock in the interest rate. This removes the uncertainty associated with market rate fluctuations between now and the borrowing date.
Speculation
Traders can use FRAs to speculate on the movement of the reference rate. A speculator who believes the market rate will be higher than the current FRA rate should **buy** the FRA. If they believe the market rate will be lower, they should **sell** the FRA.
FRA vs. Interest Rate Futures
While both FRAs and Interest Rate Futures (e.g., Eurodollar futures) are used to manage future interest rate risk, they differ in market structure and liquidity.
Market Differences
FRA: OTC contract, customizable notional principal and maturity dates, higher counterparty risk, settled in cash.
FRAs are preferred by large institutional users who require tailored contracts not available on exchanges, despite the higher counterparty risk.
Conclusion
The Forward Rate Agreement (FRA) is an essential OTC instrument for managing short-term interest rate risk. Its pricing (the FRA rate) is derived from the **yield curve** to ensure initial pricing is fair.
The payoff is a cash settlement determined by the difference between the contracted FRA rate and the actual market reference rate on the **fixing date**. FRAs provide corporate hedgers with the crucial ability to lock in financing costs for future periods with precise customizability.
Frequently Asked Questions
Common questions about Forward Rate Agreements and settlement
What is a Forward Rate Agreement (FRA)?
A Forward Rate Agreement is an over-the-counter derivative contract that locks in an interest rate for a future period. It's an agreement between two parties where one will pay a fixed rate and receive a floating rate (or vice versa) on a notional principal amount for a specified future time period. No principal is exchanged—only the net settlement based on rate differences.
How does FRA settlement work?
Settlement occurs at the start of the contract period (not the end). The party paying fixed receives the difference if market rates rise above the agreed rate. The payment is discounted to present value since interest accrues over the period. The formula accounts for the time difference between settlement and the end of the interest period.
What are common FRA maturities and conventions?
FRAs are quoted as "start x end" (e.g., "6x9 FRA" means starts in 6 months, covers next 3 months). Common periods include 1x4, 3x6, 6x9, 6x12, and 12x24 months. They typically reference LIBOR, SOFR, or other interbank rates. Market convention uses actual/360 or actual/365 day count methods.
Who uses FRAs and why?
Banks, corporations, and investors use FRAs to hedge against interest rate changes on future borrowing or investments, to lock in funding costs, to speculate on interest rate movements, and to manage gaps between assets and liabilities. They're particularly useful for managing exposure to floating-rate obligations.
What are the advantages of FRAs over futures?
Advantages include customization of notional and dates, no margin requirements, over-the-counter flexibility, and credit relationship between counterparties. However, FRAs lack exchange clearing and may involve counterparty credit risk. Futures offer standardization, central clearing, and daily margining.
How do I interpret a positive vs negative settlement?
A positive settlement means the party paying fixed receives payment when market rates are higher than the agreed rate, while a negative settlement means they pay when market rates are lower than the agreed rate. The long position benefits when rates rise, while the short position benefits when rates fall. Settlement flows from the perspective of the long position.
What risks are associated with FRAs?
Risks include counterparty credit risk (default), market risk (unexpected rate movements), basis risk (reference rate mismatch), settlement risk, and liquidity risk. Credit risk is typically managed through credit limits, collateral, and credit default swaps. Market risk is offset by taking opposite positions.
How are FRAs priced and what affects their value?
FRA prices (forward rates) are derived from spot rates using the interest rate parity concept. The forward rate is the rate that makes investing for the long period equivalent to investing for short period and rolling over. Factors affecting value include changes in forward curve, credit spreads, time to settlement, and volatility.
Can FRAs be used for speculation?
Yes. Speculators can take positions in FRAs based on their interest rate views. Buying (going long) FRAs profits if rates rise above the agreed rate. Selling (going short) FRAs profits if rates fall below the agreed rate. Unlike hedgers, speculators have no underlying exposure to offset, creating directional risk.
How do FRAs relate to interest rate swaps?
A swap is essentially a series of FRAs packaged together. An interest rate swap can be decomposed into a strip of forward rate agreements. The relationship is that each swap fixed-rate payment can be priced as the average of the corresponding forward rates, adjusted for payment frequency and day count conventions.
Summary
FRAs lock in interest rates for future borrowing or lending periods.
Settlement is based on the difference between agreed and market rates.
Useful for hedging short-term interest rate risk with OTC flexibility.
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Frequently asked questions
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