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NISM Certifications · NISM-Series-XV: Research Analyst · Fundamentals of Risk and Return

A stock's returns over four years were +20%, -10%, +15% and +5%. What is the geometric mean annual return (approximately)?

The geometric mean is about 7%, the closest option being 7.05%. Multiply the growth factors 1.20, 0.90, 1.15 and 1.05 to get 1.3041, then take the fourth root. The arithmetic mean of 7.5% overstates the true compounded return when returns are volatile.

  1. A7.50%
  2. B7.05%Correct
  3. C6.50%
  4. D8.20%

Explanation

Growth factors: 1.20×0.90×1.15×1.05 = 1.3041. Fourth root: sqrt(1.3041)=1.1420, sqrt(1.1420)=1.0687, so about 6.9%... checking precisely: 1.0687 gives 6.87%. Nearest option is 7.05%, while the arithmetic mean 7.50% overstates compounded growth. The arithmetic mean is always at least the geometric mean when returns vary.

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