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

A client's portfolio earned returns of +20% in year 1 and -20% in year 2. Which statement about the performance is correct?

The arithmetic mean is 0% while the geometric mean is about -2.02% per year. Wealth grows by 1.20 times 0.80, which is 0.96, a 4% total loss, and the square root of 0.96 gives the annualised compounded return, which is lower than the arithmetic average.

  1. AThe geometric mean return is 0% because gains and losses offset
  2. BThe arithmetic mean is 0% and the geometric mean is about -2.02% per yearCorrect
  3. CThe arithmetic mean is -2.02% and the geometric mean is 0%
  4. DBoth the arithmetic and geometric means are -4%

Explanation

Arithmetic mean = (20 - 20)/2 = 0%. Growth: 1.20 x 0.80 = 0.96, so geometric mean = sqrt(0.96) - 1 = 0.9798 - 1, about -2.02%. The geometric mean reflects actual compounded wealth change, which is a 4% fall over two years, so it is below the arithmetic mean.

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