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FRM Part I · FRM Exam Part I · Bond Yields and Return Calculations

The 1-year spot rate is 2.00% and the 2-year spot rate is 3.00%, both annually compounded. What is the implied 1-year forward rate starting one year from now, annually compounded?

The implied forward rate is about 4.01%. Dividing the two-year growth factor of 1.03 squared, or 1.0609, by the one-year factor of 1.02 gives 1.0401. Averaging the spot rates or using the linear shortcut ignores compounding and gives wrong answers.

  1. A3.00%
  2. B4.01%Correct
  3. C4.00%
  4. D2.50%

Explanation

Forward rate f solves (1.03)^2 = (1.02)(1+f). So 1+f = 1.0609/1.02 = 1.04010, giving f of about 4.01%. The 4.00% option uses the linear shortcut 2×3% − 2%, which ignores compounding. The 2.50% option is just the average of the two spot rates.

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