FRM Part I · FRM Exam Part I · Properties of Interest Rates
A zero-coupon bond has a continuously compounded 2-year spot rate of 4% and a continuously compounded 3-year spot rate of 5%. What is the continuously compounded forward rate for the third year?
The forward rate for year three is 7.00%. With continuous compounding, the three-year total return of 15% less the two-year total return of 8% leaves 7% earned in the third year. Averaging the spot rates would wrongly give 4.5%.
- A4.50%
- B6.00%
- C7.00%Correct
- D9.00%
Explanation
Forward = (5% x 3 - 4% x 2)/(3 - 2) = 15% - 8% = 7%. The 4.50% option is the simple average of the spot rates, ignoring that the three-year rate is an average over the years. 9% results from adding rather than subtracting incorrectly.
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