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

Two returns of a stock over a two-year period are +50% in year 1 and -20% in year 2. What is the approximate geometric mean (compound annual) return?

The geometric mean return is about 9.5% per year. Compounding 1.5 and 0.8 gives 1.20 over two years, and the square root of 1.20 is about 1.095, so the annual compound return is roughly 9.5%, lower than the 15% arithmetic average.

  1. A15.0%
  2. B9.5%Correct
  3. C30.0%
  4. D12.5%

Explanation

Growth factor = 1.5 x 0.8 = 1.20. Geometric mean = sqrt(1.20) - 1 = 1.0954 - 1 = about 9.5%. The arithmetic mean of 15% overstates the compound return, which is the key mistake in the first option.

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