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FRM Part I · FRM Exam Part I · Properties of Interest Rates

The 2-year continuously compounded zero rate is 4.0% and the 5-year continuously compounded zero rate is 5.0%. What is the implied continuously compounded forward rate between year 2 and year 5?

The implied forward rate is about 5.67%. Five years at 5% accumulates 25% of log return, two years at 4% accounts for 8%, leaving 17% to be earned over the three years in between, which is 5.67% per year.

  1. A5.67%Correct
  2. B4.50%
  3. C3.40%
  4. D5.00%

Explanation

Forward = (5.0%*5 - 4.0%*2)/(5-2) = (25 - 8)/3 = 5.67%. The 3.40% option divides 17 by 5 instead of 3, using the wrong time span. The 4.50% option averages the two zero rates and ignores the weighting by maturity.

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