Annualized Return Calculator — Geometric Mean of Annual Returns
Enter annual returns as percentages, separated by commas
Used to show dollar growth; does not affect return calculations
Annualized Return (Geometric Mean)
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Arithmetic Mean Return
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Cumulative Return
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Standard Deviation (Volatility)
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Final Portfolio Value
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Number of Periods
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How to Calculate Annualized Returns from a Series of Annual Returns
When you have a sequence of annual returns — say your portfolio gained 12% one year, lost 5% the next, and gained 18% the year after — the annualized return tells you the single constant rate that would produce the same cumulative result. This is the geometric mean return, and it is the standard way professionals measure investment performance over multiple periods.
The geometric mean is calculated by multiplying together (1 + each return), taking the Nth root of the product (where N is the number of periods), and subtracting 1. For example, with returns of +10% and -10%, the product is 1.10 × 0.90 = 0.99, the square root is 0.995, and the annualized return is -0.50% — not zero, as a simple average would suggest. This difference, called volatility drag, is why the geometric mean is always the correct measure for compounded performance.
This calculator also shows the arithmetic mean (simple average), which is useful for estimating expected return in any single future year, and the standard deviation, which measures how much returns vary from year to year. Together, the annualized return, arithmetic mean, and volatility give you a complete picture of an investment's historical risk-return profile.
Frequently Asked Questions
What is the difference between arithmetic and geometric mean return?
The arithmetic mean is a simple average of annual returns, while the geometric mean accounts for compounding. The geometric mean is always less than or equal to the arithmetic mean when returns vary, and it represents the actual annualized growth rate of your investment. For example, if an investment gains 50% one year and loses 50% the next, the arithmetic mean is 0%, but the geometric mean is -13.4% — reflecting the actual loss.
Why is the geometric mean return lower than the arithmetic mean?
This is due to volatility drag (also called variance drain). The more volatile the returns, the greater the gap between the arithmetic and geometric means. This happens because percentage losses require larger percentage gains to recover. The geometric mean captures this compounding reality while the arithmetic mean does not.
How do I use annualized returns to compare investments?
The geometric mean (annualized) return is the best single number for comparing investment performance over time. It tells you the equivalent constant annual return that would produce the same cumulative result. Compare the annualized return alongside the standard deviation to understand both performance and risk.
Can I enter negative annual returns?
Yes. Negative returns represent years where the investment lost value. Enter them as negative percentages (e.g., -20 for a 20% loss). The calculator handles negative returns correctly, as long as no single return is -100% or worse, which would represent a total loss.