FRM Part I · FRM Exam Part I · Properties of Interest Rates
The continuously compounded zero rates are 4.0% for 1 year and 4.5% for 2 years. What is the continuously compounded forward rate for the second year, and what is the 1-year-forward rate with annual compounding (nearest 0.01%)?
The second-year forward rate is 5.00% continuously compounded, which equals 5.13% with annual compounding. Continuous forward = (0.045×2 - 0.04×1)/1 = 5%, and converting uses e^0.05 - 1 = 5.13%. Averaging the zero rates would wrongly give 4.25% or 4.5%.
- A5.00% continuous; 5.13% annualCorrect
- B4.50% continuous; 4.60% annual
- C5.00% continuous; 5.00% annual
- D4.25% continuous; 4.34% annual
Explanation
Forward = (4.5%×2 - 4.0%×1)/(2-1) = 9.0% - 4.0% = 5.00% continuous. Annual-compounding equivalent = e^0.05 - 1 = 5.127%, about 5.13%. Option with 5.00% annual forgets to convert compounding conventions.
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