The geometric average rate of return is a method of calculating the average rate of return of an investment over a period of time, taking into account the effects of compounding. It is considered a more accurate measure of performance than the arithmetic average, especially when returns fluctuate significantly.
Understanding Geometric Average Return
Unlike the arithmetic mean, which simply averages the returns, the geometric mean reflects the actual year-to-year performance of an investment. It does this by considering the compound effect of returns. This is especially important when comparing investments over multiple periods. A high arithmetic average can be misleading if there are substantial year-to-year swings in returns, as it doesn't accurately reflect the sequence of returns and their impact on the overall growth of the investment.
How to Calculate Geometric Average Return
The geometric average return is calculated as follows:
- Convert percentage returns to decimals and add 1: If the return is, say, 10%, convert it to 0.10 and add 1, resulting in 1.10. This represents the growth factor for that period.
- Multiply all the growth factors together: Multiply the growth factors for each period within the investment timeframe.
- Raise the product to the power of (1/n): Where 'n' is the number of periods (e.g., years). This finds the nth root of the product.
- Subtract 1: This converts the result back into a rate of return.
- Convert to percentage: Multiply by 100 to express the result as a percentage.
Formula:
Geometric Average Return = [ (1 + Return₁) (1 + Return₂) ... * (1 + Returnₙ) ]^(1/n) - 1
Where:
- Return₁, Return₂, ... Returnₙ are the returns for each period.
- n is the number of periods.
Example
Let's say you have an investment with the following annual returns over three years:
- Year 1: 10%
- Year 2: 20%
- Year 3: -5%
Calculation:
- Convert to decimals and add 1:
- Year 1: 1.10
- Year 2: 1.20
- Year 3: 0.95
- Multiply the growth factors: 1.10 1.20 0.95 = 1.254
- Raise to the power of (1/n): 1.254^(1/3) = 1.0773
- Subtract 1: 1.0773 - 1 = 0.0773
- Convert to percentage: 0.0773 * 100 = 7.73%
Therefore, the geometric average return for this investment is 7.73%.
Why is Geometric Average Important?
- Accurate Representation: Provides a more realistic measure of an investment's actual performance, especially for volatile investments.
- Long-Term Planning: Useful for projecting long-term investment growth.
- Comparative Analysis: Allows for a more accurate comparison of different investment options.
- Reduces Misleading Impressions: Avoids the inflated perception of returns that can result from using the arithmetic average when returns are highly variable.
In summary, the geometric average rate of return offers a more precise reflection of investment performance than the arithmetic average by accounting for the effects of compounding, making it a valuable tool for investors.
