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

Mr. Iyer invested Rs 1,00,000 in a fund. Returns in three successive years were +20%, -10% and +25%. What is the approximate compound annual (geometric) return, and what is the arithmetic mean return?

Geometric return is about 10.5% and arithmetic mean is 11.67%. Multiplying the yearly growth factors gives 1.35, whose cube root is about 1.105, while the simple average of the three returns is 11.67%. Geometric is lower because of volatility.

  1. AGeometric about 10.5%; arithmetic 11.67%Correct
  2. BGeometric about 11.67%; arithmetic 10.5%
  3. CGeometric about 10.5%; arithmetic 10.5%
  4. DGeometric about 12.5%; arithmetic 11.67%

Explanation

Arithmetic mean = (20 - 10 + 25)/3 = 11.67%. Terminal value factor = 1.20 x 0.90 x 1.25 = 1.35. Geometric mean = 1.35^(1/3) - 1, about 1.105 - 1 = 10.5% (1.105^3 is about 1.349). The geometric mean is always below the arithmetic mean when returns vary, which rules out the options that reverse or equate them.

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