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NISM Certifications · NISM-Series-XXI-A: Portfolio Management Services (PMS) Distributors · Investments

A portfolio has returns of 10%, -5% and 20% in three consecutive years. Approximately which of the following is true about its arithmetic mean return and its compound annual growth rate (CAGR)?

The arithmetic mean is 8.33% while the CAGR is lower, about 7.8%. Compounding 1.10, 0.95 and 1.20 gives 1.254, and its cube root is below 1.0833. Geometric returns are always below the arithmetic mean when returns vary.

  1. AArithmetic mean is 8.33% and CAGR is higher than that
  2. BArithmetic mean is 8.33% and CAGR is lower than thatCorrect
  3. CArithmetic mean is 5% and CAGR is equal to it
  4. DArithmetic mean is 11.67% and CAGR is lower than that

Explanation

Arithmetic mean = (10 - 5 + 20)/3 = 8.33%. Growth factor = 1.10 x 0.95 x 1.20 = 1.254, so CAGR = 1.254^(1/3) - 1, about 7.8%. With variable returns the geometric mean is below the arithmetic mean.

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