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

The 1-year continuously compounded spot rate is 3.0% and the 3-year continuously compounded spot rate is 4.0%. What is the implied continuously compounded forward rate for the period from year 1 to year 3?

The forward rate is 4.5%. Total 3-year return is 12% (4% × 3), of which 3% was earned in the first year. The remaining 9% is earned over two years, giving 4.5% per year under continuous compounding.

  1. A4.5%Correct
  2. B4.0%
  3. C5.0%
  4. D3.5%

Explanation

With continuous compounding, f = (4.0%×3 − 3.0%×1)/(3 − 1) = 9.0%/2 = 4.5%. Check: 3% + 2×4.5% = 12% = 4%×3. The 4.0% option wrongly reuses the 3-year spot rate. The 5.0% option divides by 1 instead of 2 years.

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