Geometric Mean Rate of Return Calculator
Enter the annual rates of return for each period below. The calculator will compute the geometric mean rate of return, which is a more accurate measure of average investment performance over multiple periods than the arithmetic mean.
Understanding the Geometric Mean Rate of Return
The geometric mean rate of return is a measure of the average growth rate of an investment over a period of time, considering compounding. Unlike the arithmetic mean, which simply averages the returns, the geometric mean accounts for the effect of volatility and the compounding of returns across multiple periods. This makes it a more realistic and accurate representation of an investment's actual performance.
Why is it Important?
When you invest money, the returns in subsequent periods are applied to the new, larger (or smaller) balance. For example, if you have $100 and it grows by 10% in Year 1 to $110, and then by 20% in Year 2, your Year 2 return is applied to $110, not the initial $100. The geometric mean accurately reflects this compounding effect. If you were to simply average a 10% and a 20% return, you'd get 15%. However, the actual compounded return over two years would be different.
How it's Calculated
The formula for the geometric mean rate of return (G) for 'n' periods is:
G = [(1 + R1) * (1 + R2) * … * (1 + Rn)]^(1/n) – 1
Where:
- R1, R2, …, Rn are the individual period rates of return (expressed as decimals).
For example, a 10% return is entered as 0.10, and a -5% return is entered as -0.05.
Example Calculation
Let's consider an investment with the following annual returns:
- Year 1: 10%
- Year 2: 20%
- Year 3: 5%
- Year 4: -8%
- Year 5: 15%
Using the calculator, you would input 10, 20, 5, -8, and 15.
The calculation would be:
G = [(1 + 0.10) * (1 + 0.20) * (1 + 0.05) * (1 – 0.08) * (1 + 0.15)]^(1/5) – 1
G = [1.10 * 1.20 * 1.05 * 0.92 * 1.15]^(1/5) – 1
G = [1.546008]^(1/5) – 1
G = 1.0908 – 1
G = 0.0908 or 9.08%
The geometric mean rate of return for this investment is approximately 9.08%. This is the steady annual rate that would have resulted in the same final investment value over the five-year period.