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CFA Level I · CFA Level I Exam · Statistical Characteristics of Asset Returns

A portfolio had annual returns of +20%, -10% and +20% over three years. The geometric mean annual return is closest to:

The geometric mean return is about 9%, so the closest option is 8.5%. Multiply the growth factors 1.20, 0.90 and 1.20 to get 1.296, then take the cube root. The 10% figure is the arithmetic mean, which ignores compounding.

  1. A8.5%Correct
  2. B10.0%
  3. C12.0%

Explanation

Growth factors: 1.20 x 0.90 x 1.20 = 1.296. Cube root of 1.296 is about 1.0914, since 1.0914^3 is about 1.300; more precisely 1.0901^3 = 1.2955, so the rate is about 9.0%. Checking the options, 8.5% would give 1.277 and 10% would give 1.331, so 8.5% is the closest to 9.0%. The 10.0% option is the arithmetic mean (20-10+20)/3 = 10.0%, which is the mistake of ignoring compounding.

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