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NISM Certifications · NISM-Series-X-A: Investment Adviser (Level 1) · Introduction to Investment

An investment's returns in three successive years were +20%, -10% and +25%. What is the geometric mean annual return, approximately, and how does it compare with the arithmetic mean of 11.67%?

The geometric mean return is about 10.5%, lower than the arithmetic mean of 11.67%. Multiplying growth factors 1.20, 0.90 and 1.25 gives 1.35, and its cube root is about 1.105. Geometric mean is always below arithmetic mean when returns fluctuate.

  1. AApproximately 11.67%, equal to the arithmetic mean
  2. BApproximately 10.5%, lower than the arithmetic meanCorrect
  3. CApproximately 13.5%, higher than the arithmetic mean
  4. DApproximately 8.0%, lower than the arithmetic mean

Explanation

Growth factor = 1.20 x 0.90 x 1.25 = 1.35. The cube root of 1.35 is about 1.1052, so the geometric mean is about 10.5%. Geometric mean is below the arithmetic mean when returns vary. Check: 1.105^3 is about 1.349. The 13.5% option is wrongly derived from total return 35% divided by about 2.6, and 8.0% results from an unsupported calculation.

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