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

The continuously compounded zero rates are 3.0% for 1 year and 3.6% for 2 years. What is the continuously compounded forward rate for the period from year 1 to year 2?

The forward rate is 4.2% continuously compounded. It equals the 2-year zero rate times 2 (7.2%) minus the 1-year zero rate times 1 (3.0%), divided by the one-year gap between them. Simply averaging the two zero rates would give a wrong answer.

  1. A3.3%
  2. B4.2%Correct
  3. C3.6%
  4. D2.4%

Explanation

Forward rate = (R2*T2 - R1*T1)/(T2-T1) = (3.6*2 - 3.0*1)/1 = 7.2 - 3.0 = 4.2%. The 3.3% option is the simple average of the two zero rates, which ignores the longer time weighting on the 2-year rate. The 2.4% option comes from reversing the sign on the 1-year term.

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