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

A bond fund returns +20%, −10% and +5% in three consecutive years. What is its geometric average annual return (closest figure)?

The geometric average annual return is about 4.28%. Multiplying the growth factors 1.20, 0.90 and 1.05 gives 1.134 cumulative growth, and the cube root of that minus 1 is 4.28%. The arithmetic mean of 5% overstates the compound return.

  1. A4.28%Correct
  2. B5.00%
  3. C4.50%
  4. D13.40%

Explanation

Cumulative growth = 1.20 × 0.90 × 1.05 = 1.134. Geometric average = 1.134^(1/3) − 1 ≈ 4.28%. The 5.00% figure is the arithmetic mean, which overstates compound growth. The 13.40% figure is the cumulative return, not an annual average.

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