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

A research analyst computes the arithmetic mean of an equity's annual returns over several years and also its geometric mean return. When annual returns vary from year to year, which statement about the two measures is correct?

The geometric mean is lower than the arithmetic mean when returns vary, and it reflects compounded growth. It measures the actual per-period growth of wealth, while the two measures coincide only if every period's return is identical.

  1. AThe geometric mean is always higher than the arithmetic mean
  2. BThe geometric mean is lower than the arithmetic mean, and it reflects compounded growthCorrect
  3. CThe two are always equal
  4. DThe arithmetic mean reflects compounding while the geometric mean ignores it

Explanation

When returns are volatile, the geometric mean is lower than the arithmetic mean. The geometric mean captures the effect of compounding and so represents the actual growth of wealth. The two are equal only when all returns are identical.

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