Explain how the rate on an interest rate forward contract is fixed
The idea
An interest rate forward, or forward rate agreement, fixes today a rate that will apply to a future period on a notional principal. The fixed rate is set so that the contract has zero value at initiation, which means it must equal the implied forward rate from today's spot rates; any other rate would allow an arbitrage by borrowing for one period and lending for another. With annual compounding, the one-year rate one year forward is (1 + S2)² / (1 + S1) - 1. For money-market periods, the forward rate for days a to b is [(1 + Rb x b/360) / (1 + Ra x a/360) - 1] x 360 / (b - a). A long FRA pays the fixed rate and receives the floating rate, so it gains when rates rise and is used by a future borrower to lock in borrowing costs; a short FRA suits a future lender. The settlement payment is the rate difference on notional for the period, discounted at the reference rate.
A practice question
A company will borrow at a floating rate in three months and fears rates will rise. To lock in its rate using an FRA, it should:
- take a long position in the FRA — correct
- take a short position in the FRAWhy not: A short FRA gains when rates fall, which suits a future lender, not a borrower.
- take no position until rates riseWhy not: Waiting leaves the exposure unhedged, which is what the company wants to avoid.
A long FRA pays fixed and receives floating, so its gain when rates rise offsets the company's higher borrowing cost.
A harder one
The one-year spot rate is 3.0% and the two-year spot rate is 4.0%, both annually compounded. What is the implied one-year rate one year from now?
- 3.50%Why not: Averages the two spot rates, which gives something between them rather than the forward.
- 4.00%Why not: Uses the two-year spot rate, ignoring that the first year earns only 3%.
- 5.01% — correct
Forward = 1.04^2 / 1.03 - 1 = 1.0816 / 1.03 - 1 = 5.01%. Investing for two years at 4% must equal one year at 3% followed by one year at the forward rate.
The hardest tier
A long 3x6 FRA on 10 million notional has a fixed rate of 3.0%. At settlement the 90-day reference rate is 3.5% (360-day basis). What does the long receive at settlement?
- 12,500Why not: Correct interest difference, but not discounted back from the end of the 90-day period.
- 12,392 — correct
- 50,000Why not: Applies the full annual rate difference, omitting the 90/360 day-count fraction.
Interest difference = (0.035 - 0.030) x 90/360 x 10,000,000 = 12,500, paid at the start of the period, so discount it: 12,500 / (1 + 0.035 x 90/360) = 12,392.
In the app: 6 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
Take the free diagnostic →