Definition
The geometric mean is the mathematically correct way to calculate average investment returns over time. Unlike the arithmetic mean, it accounts for compounding and volatility drag. The geometric mean is always less than or equal to the arithmetic mean, with the difference increasing with volatility. It represents the actual growth rate of invested capital.
functions Formula
Geometric Mean = (Π(1 + Ri))^(1/n) − 1
lightbulb Example
Returns over 3 years: +20%, -10%, +15%. Arithmetic mean = 8.33%. Geometric mean = (1.20 × 0.90 × 1.15)^(1/3) − 1 = 7.53%. The geometric mean correctly reflects the actual growth of $100 to $124.20.
verified_user Key Points
- Correctly measures compound investment returns
- Always ≤ arithmetic mean
- Difference increases with volatility
- The actual growth rate of invested capital