Geometric Mean Return Calculator

Geometric Mean Formula:

\[ \text{Geometric Mean} = \left[(1 + R_1) \times (1 + R_2) \times \cdots \times (1 + R_n)\right]^{1/n} - 1 \]

Geometric Mean Return:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Geometric Mean Return?

The geometric mean return calculates the average rate of return for investments that compound over multiple periods. It accounts for the volatility and compounding effect, providing a more accurate measure of investment performance than simple arithmetic mean.

2. How Does the Calculator Work?

The calculator uses the geometric mean formula:

\[ \text{Geometric Mean} = \left[(1 + R_1) \times (1 + R_2) \times \cdots \times (1 + R_n)\right]^{1/n} - 1 \]

Where:

\( R_i \) — Return for period i (in decimal form, e.g., 0.05 for 5%)
\( n \) — Number of periods

Explanation: The formula multiplies all the period returns (after adding 1 to each), takes the nth root of the product, then subtracts 1 to get the average compounded return per period.

3. Importance of Geometric Mean

Details: The geometric mean is essential for understanding investment performance because it accounts for the compounding effect of returns over time. It's particularly important when returns are volatile, as it properly weights the sequence of returns.

4. Using the Calculator

Tips: Enter the periodic returns as comma-separated decimal values (e.g., 0.05, -0.02, 0.1 for 5%, -2%, 10%). The calculator will ignore any non-numeric values.

5. Frequently Asked Questions (FAQ)

Q1: Why use geometric mean instead of arithmetic mean for returns?
A: Geometric mean accounts for compounding and volatility, giving the actual average return an investor would earn over time. Arithmetic mean overstates performance when returns vary.

Q2: When should I use geometric mean?
A: Use it when analyzing compounded investment returns over multiple periods, especially when comparing different investments or strategies.

Q3: What does a negative geometric mean indicate?
A: It means the investment lost value on average during the measured periods, with compounding effects considered.

Q4: How does volatility affect geometric mean?
A: Higher volatility (with the same arithmetic mean) results in a lower geometric mean due to the greater impact of negative returns when compounded.

Q5: Can I use this for percentage returns directly?
A: No, you must convert percentages to decimals (e.g., 5% = 0.05) before entering them into the calculator.