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

A bond portfolio earns a total return of 1.20% over a three-month period. If that quarterly return is repeated for four consecutive quarters with compounding, what is the equivalent annual effective return (closest figure)?

The equivalent annual effective return is about 4.89%. Compounding the 1.20% quarterly return four times gives 1.012 to the fourth power, or 1.04887. Simple multiplication would understate it at 4.80%, and the log return would be 4.77%.

  1. A4.89%Correct
  2. B4.80%
  3. C4.77%
  4. D2.41%

Explanation

Annual effective return = (1.012)^4 − 1. Since 1.012^2 = 1.024144, squaring gives 1.04887, i.e. 4.89%. The 4.80% figure is simple multiplication with no compounding. The 4.77% figure is the continuously compounded rate, 4 × ln(1.012). The 2.41% figure compounds only twice.

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