FRM Part I · FRM Exam Part I · Interest Rates
The 1-year spot rate is 2.00% and the 2-year spot rate is 3.00%, both with annual compounding. What is the implied 1-year forward rate starting one year from now (the 1y1y forward rate)?
The implied 1y1y forward rate is about 4.01%. Investing for two years at the 3% spot must equal investing one year at 2% and then rolling at the forward rate, so 1.0609 divided by 1.02 gives 1.0401. Averaging spot rates understates the forward.
- A4.01%Correct
- B3.50%
- C3.00%
- D2.50%
Explanation
No-arbitrage requires (1.02)(1+f) = (1.03)^2 = 1.0609. So 1+f = 1.0609/1.02 = 1.04010, giving f = 4.01%. 3.50% is wrong because it is a naive average of the two spot rates. 3.00% just repeats the 2-year spot rate.
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