Updated for the 2026-2027 CFA® Level I curriculum.
An interest rate forward contract locks in a rate for borrowing or lending money at a future date. The most common version, the forward rate agreement (FRA), settles in cash based on the difference between an agreed fixed rate and a reference rate observed later. CFA Level I tests whether you can derive the forward rate implied by today's spot rates and explain why a borrower or lender would use one. After this note, you should be able to calculate an implied forward rate and interpret an FRA quote correctly.
Quick Answer
A forward rate agreement (FRA) is a contract that locks in an interest rate for a loan or deposit that begins on a future date. The rate is set today using the no-arbitrage forward rate, which is the rate that makes investing long term equal to investing short term and rolling over at the forward rate. Borrowers buy FRAs to hedge against rising rates. Lenders sell FRAs to hedge against falling rates. No principal changes hands, only a cash settlement tied to the rate difference.
Key Takeaways About Interest Rate Forward Contracts and Forward Rates
A forward rate agreement (FRA) fixes an interest rate today for a loan or deposit period that starts in the future.
The forward rate is derived from spot rates using a no-arbitrage relationship, not a forecast of the future spot rate.
FRA maturities are described with two numbers, such as "3x6," meaning the contract starts in 3 months and ends in 6 months.
No notional principal is exchanged. Settlement is a single cash payment based on the rate difference.
A borrower who fears rising rates buys (goes long) an FRA. A lender who fears falling rates sells (goes short) an FRA.
FRA settlement happens at the start of the underlying interest period, so the payment is discounted back from the end of the period.
A common error is treating the forward rate as a prediction. It is a break-even rate implied by current spot rates.
What You Need to Know for CFA Level I
Identify what an interest rate forward or FRA locks in: a rate, not a price or a bond value.
Calculate a forward rate implied by two spot rates using the no-arbitrage compounding relationship.
Apply the no-arbitrage relationship across different maturities without mixing up the time periods.
Distinguish the borrower's use of an FRA (long, hedges rising rates) from the lender's use (short, hedges falling rates).
Read an FRA quote correctly, including the start date, end date, and underlying reference period.
Recognize that FRA settlement occurs at the start of the interest period, not the end.
What Is an Interest Rate Forward Contract?
An interest rate forward contract is an agreement between two parties to exchange a fixed interest rate for a floating reference rate on a set notional amount, for a set period, starting on a future date. The underlying is an interest rate, not a security price.
The most widely tested version is the forward rate agreement (FRA). One party agrees to pay a fixed rate. The other agrees to pay a floating reference rate, typically a market reference rate observed at the start of the underlying period. Because both payments are based on the same notional and the same period, the parties do not exchange the notional itself. They exchange only the difference in interest, in cash, at settlement.
The buyer of the FRA is long. The buyer profits if the reference rate at settlement is above the FRA rate. The seller is short and profits if the reference rate is below the FRA rate.
What Is a Forward Rate?
A forward rate is the interest rate for a future period that is implied by today's spot rates. It is not a forecast. It is the rate that removes arbitrage between two ways of investing over the same total horizon.
Consider two choices for investing money for two years:
Invest directly for two years at the two-year spot rate.
Invest for one year at the one-year spot rate, then reinvest the proceeds for a second year at whatever rate is available then.
For these two choices to produce the same result with no arbitrage opportunity, the market must imply a specific rate for that second year. That implied rate is the forward rate.
How Forward Rates Are Determined
The forward rate is set so that a longer-term spot investment produces the same result as a shorter-term spot investment rolled into a forward-rate investment. For periods measured in whole years with annual compounding:
Where:
= spot rate for the longer period,
= spot rate for the shorter period,
= forward rate for the period beginning at and ending at
and are expressed in years, with greater than
FRAs typically use money market instruments with maturities in days rather than years. Money market rates are quoted on a simple interest, actual/360 basis. The same no-arbitrage logic applies, adjusted for day counts:
Where:
= spot money market rate for days
= spot money market rate for days
FRA(B, A-B) = the forward rate agreement rate for the period starting in days and ending in days
The logic is identical in both versions. A longer investment must equal a shorter investment plus a forward-rate investment covering the remaining time.
Forward Rate Agreement Mechanics
FRAs are quoted using two numbers separated by an "x," such as "3x6" or "1x4."
FRA Quote | Contract Start | Contract End | Underlying Period |
|---|---|---|---|
1x4 | 1 month | 4 months | 3-month rate |
3x6 | 3 months | 6 months | 3-month rate |
6x12 | 6 months | 12 months | 6-month rate |
Three features define FRA mechanics:
No principal exchange. The notional amount only determines the size of the interest calculation. It is never paid or received.
Cash settlement at the start of the period. Interest is normally paid at the end of a loan period, but the FRA settles at the beginning. The payment is calculated as if paid at the end, then discounted back to the settlement date using the reference rate observed at settlement.
Payoff direction. The long position (fixed-rate payer) receives a payment if the reference rate is above the FRA rate. The short position (fixed-rate receiver) receives a payment if the reference rate is below the FRA rate.
How Borrowers and Lenders Use Forward Rates
Forward rates give borrowers and lenders a way to fix a future rate before the loan or deposit period begins.
Party | Concern | FRA Position | Outcome if Rates Rise | Outcome if Rates Fall |
|---|---|---|---|---|
Borrower | Rising rates increase borrowing cost | Long FRA (pays fixed) | Gains on FRA offsets higher borrowing cost | Loses on FRA, but borrows at lower market rate |
Lender or investor | Falling rates reduce investment income | Short FRA (receives fixed) | Loses on FRA, but reinvests at higher market rate | Gains on FRA offsets lower reinvestment rate |
The FRA does not remove the underlying loan or deposit. It only offsets the change in the interest rate. The borrower still borrows at the market rate and still faces the lender's credit terms. The FRA payment adjusts the net cost.
Interpreting an FRA Quote
An FRA quote combines three pieces of information: when the contract starts, when it ends, and what period it covers.
A "3x9 FRA at 3.50%" means:
The contract starts in 3 months.
The contract ends in 9 months.
The underlying reference period is 6 months (9 minus 3).
The fixed rate agreed today is 3.50% annualized.
At the 3-month mark, the parties compare the 6-month reference rate observed in the market to 3.50%. The difference, adjusted for the notional and discounted to the settlement date, determines the payment.
Worked Example
A treasury analyst wants to know the market's implied rate for a 90-day loan starting in 90 days. The following money market spot rates are observed today, quoted on an actual/360, add-on basis:
90-day rate: 2.50%
180-day rate: 3.00%
Step 1: Set up the no-arbitrage equation.
Step 2: Solve the known terms.
Step 3: Isolate the forward rate term.
The market implies a 90-day rate of about 3.48% for the period starting 90 days from now. This is the rate for a "3x6" FRA. A company planning to borrow for 90 days, three months from now, can buy this FRA today to lock in a borrowing cost near 3.48%, regardless of where market rates move in the meantime.
If the actual reference rate at settlement is higher than 3.48%, the FRA pays the borrower the difference, offsetting the higher borrowing cost.
Common Exam Traps
Treating the forward rate as a rate forecast
The forward rate is a break-even rate implied by no-arbitrage pricing today. It is not the market's prediction of where rates will actually be.
Mismatching the maturity periods
The forward-rate formula requires the correct exponents or day-count fractions for each period. Using the wrong period length, especially the length of the forward period itself, produces an incorrect rate.
Confusing borrower and lender exposure
A borrower hedges rising rates by going long the FRA. A lender or investor hedges falling rates by going short. Reversing this logic reverses the entire payoff interpretation.
Assuming the notional amount is exchanged
The FRA notional only scales the interest calculation. The parties settle only the interest differential, in cash, never the principal.
Practice Questions
An analyst observes the following annual effective spot rates: the 1-year rate is 4.00% and the 2-year rate is 5.00%. What is the implied 1-year forward rate one year from today?
5.00%
6.01%
7.00%
Correct Answer: B
Calculation:
The no-arbitrage relationship requires that investing for two years at the two-year spot rate produce the same result as investing for one year and rolling into the forward rate for the second year. Solving for the forward rate gives approximately 6.01%.
Option A: Uses the two-year spot rate directly instead of solving the compounding relationship. This ignores the effect of compounding over the first year.
Option C: Overstates the forward rate by doubling the spread between the two spot rates instead of applying the correct compounding formula.
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FAQs About Interest Rate Forward Contracts and Forward Rates
What is a forward rate agreement (FRA)?
An FRA is a contract that locks in an interest rate today for a loan or deposit period that begins on a future date. It settles in cash based on the difference between the agreed fixed rate and the reference rate observed at settlement.
What does a forward rate agreement example look like in practice?
A company expecting to borrow in three months might buy a 3x6 FRA to lock in a 90-day borrowing rate. If market rates rise above the FRA rate by the settlement date, the FRA pays the company the difference, offsetting the higher borrowing cost.
Does a forward rate predict future interest rates?
No. The forward rate is a break-even rate derived from today's spot rates through a no-arbitrage relationship. It does not represent a market forecast of where rates will actually move.
Is any principal exchanged when an FRA settles?
No. The notional amount is used only to calculate the interest difference. The parties exchange a single cash payment based on that difference, discounted to the settlement date.