Answer: geometric mean.

## Explanation When estimating the average return of an investment over multiple consecutive periods (time-weighted returns), the **geometric mean** is most appropriate because it accounts for the compounding effect of returns over time. ### Why Geometric Mean is Correct: 1. **Compounding Effect**: Investment returns compound over time. If you have returns of +20% in year 1 and -10% in year 2, the arithmetic mean would be 5%, but the actual cumulative return would be: - Year 1: $100 × 1.20 = $120 - Year 2: $120 × 0.90 = $108 - Total return = 8% over 2 years, not 10% (5% × 2 years) 2. **Geometric Mean Calculation**: - Geometric mean = [(1 + R₁) × (1 + R₂) × ... × (1 + Rₙ)]^(1/n) - 1 - For returns +20% and -10%: [(1.20) × (0.90)]^(1/2) - 1 = (1.08)^(0.5) - 1 ≈ 0.0392 or 3.92% - This accurately reflects the annualized return ### Why Other Means are Incorrect: - **Arithmetic Mean**: Simply averages the returns without considering compounding, which overstates the actual return when volatility is present. - **Harmonic Mean**: Used for averaging rates when the denominator varies (like average speed over equal distances), not appropriate for investment returns. ### Key Takeaway: For multi-period investment returns, always use the geometric mean to calculate the compound annual growth rate (CAGR) or time-weighted rate of return.

Author: LeetQuiz .