FRM Part I · FRM Exam Part I · Interest Rates
Continuously compounded spot rates are 4.0% for 1 year and 4.5% for 2 years. What is the continuously compounded forward rate for the period from year 1 to year 2?
The forward rate is 5.0%. With continuous compounding, the 2-year return of 9.0% (2 times 4.5%) equals the 1-year return of 4.0% plus the forward return, so the forward rate is 9.0% minus 4.0%. Averaging the spot rates would wrongly give 4.25%.
- A5.0%Correct
- B4.5%
- C4.25%
- D5.5%
Explanation
With continuous compounding, 2 x 4.5% = 4.0% x 1 + f x 1, so f = 9.0% - 4.0% = 5.0%. 4.5% just repeats the 2-year spot rate. 4.25% is the average of the two spot rates. 5.5% comes from a sign slip, using 2 x 4.5% + 4.0% - 7.5%-type errors rather than subtracting the 1-year return correctly.
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