FRM Part I · FRM Exam Part I · Pricing Conventions, Discounting, and Arbitrage
The one-year spot rate is 3.00% and the two-year spot rate is 4.00%, both annually compounded. What is the implied one-year forward rate starting one year from now (annually compounded)?
The implied one-year forward rate one year ahead is about 5.01%. It comes from (1.04)^2 divided by 1.03, minus one, because investing for two years at the spot rate must equal investing one year at spot and then rolling at the forward rate.
- A3.50%
- B4.00%
- C5.01%Correct
- D7.00%
Explanation
No-arbitrage requires (1.03)(1+f) = (1.04)^2. So 1+f = 1.0816/1.03 = 1.05010, giving f ≈ 5.01%. The 3.50% option is the simple average of the two spot rates, which ignores compounding and the way spot rates are built from forwards.
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