What does the geometric mean represent?

The geometric mean represents a method for calculating the average rate of return over time, especially useful when dealing with rates that are compounded. The correct interpretation involves the product of returns, where each return is represented as (1 + Ri). Thus, the geometric mean is calculated by taking the nth root of the product of (1 + R1), (1 + R2), and so on, through to (1 + Rt), where n is the total number of returns.

This method is particularly effective in finance because it accounts for the compounding effect that can occur with investment returns. By using the geometric mean, you can understand the compounded growth rate over multiple periods, making it a more accurate reflection of investment performance than simply using the arithmetic mean, which can be distorted by outliers or extreme values.

Using the product of returns specifically helps investors evaluate the overall return on an investment over time, considering the multiplicative nature of investment returns rather than simply averaging them. This is critical when assessing long-term investments or when returns fluctuate significantly from period to period.