CFA Level IQuantitative MethodsEasy
An analyst calculates a stock's annual returns for three consecutive years: Year 1 = 20%, Year 2 = -10%, and Year 3 = 15%. What is the stock's geometric mean annual return over the three years?
- A7.49%
- B8.33%
- C6.50%
- D7.00%
Show answer & explanationAnswer & explanation
Correct answer: A. 7.49%
Geometric mean = [(1.20)(0.90)(1.15)]^(1/3) - 1 = (1.242)^(1/3) - 1 ≈ 1.0749 - 1 = 7.49%. The arithmetic mean (8.33%) overstates true compound growth because it ignores volatility drag.
Why the other options are wrong
- B. This is the arithmetic mean (25%/3), which overstates compound growth.
- C. Too low; underestimates the actual compounded growth rate.
- D. Rounding error; does not match the correct compounded calculation.
Geometric Mean Return
The compound annual growth rate that accounts for the effects of compounding over multiple periods, calculated as the nth root of the product of (1+return) terms minus 1.
- Geometric mean ≤ arithmetic mean whenever returns vary
- Best measure for reporting historical compound performance
- Formula: [(1+R1)(1+R2)...(1+Rn)]^(1/n) - 1
Memory trick: Geometric mean grows steady, arithmetic mean floats too high