FRM Part I · FRM Exam Part I · Properties of Interest Rates
Continuously compounded zero rates are 3.0% for 1 year and 3.8% for 2 years. What is the forward rate for the second year, continuously compounded?
The forward rate for year two is 4.6%. With continuous compounding it equals the 2-year rate times 2 minus the 1-year rate times 1, divided by one year: 7.6% - 3.0%. Averaging the two zero rates to get 3.4% is wrong because the forward rate covers only the second year.
- A4.6%Correct
- B3.4%
- C3.8%
- D4.2%
Explanation
The forward rate is (3.8% × 2 - 3.0% × 1)/(2 - 1) = 7.6% - 3.0% = 4.6%. The 3.4% option is the simple average of the two zero rates. The 3.8% option just repeats the 2-year zero rate, which is the average rate over both years rather than the rate for year two alone.
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