FRM Part I · FRM Exam Part I · Properties of Interest Rates
The one-year spot rate is 3.0% and the two-year spot rate is 4.0%, both annually compounded. Under the pure expectations theory, what is the expected one-year rate one year from now (to the nearest 0.01%)?
The implied forward rate is (1.04 squared divided by 1.03) minus one, which equals about 5.01%. Under pure expectations this forward rate is the expected one-year rate a year ahead. Using 2×4% − 3% = 5.00% ignores compounding and is slightly wrong.
- A5.00%
- B5.01%Correct
- C4.50%
- D3.50%
Explanation
(1.04)^2 = 1.0816. Divide by 1.03 = 1.05010, so the forward rate is 5.01%. The 5.00% option comes from simply doubling the 2-year rate and subtracting the 1-year rate (2×4%−3%), ignoring compounding.
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