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Average Return Calculator

Calculate arithmetic mean, geometric mean, and annualized returns for your investments. Understand the true performance of your portfolio across multiple periods.

Investment Returns

Period 1
%
Years
Months
Period 2
%
Years
Months
Period 3
%
Years
Months
Total Periods
0
Spanning 0.00 years

Return Metrics

Arithmetic Mean
Simple average of returns
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Geometric Mean (CAGR)
Compound average return
+0.00%
Annualized Return
Time-weighted annual return
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Cumulative Return
Total return over all periods
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Return Comparison

Why are the values different?

Arithmetic mean is a simple average, while geometric mean accounts for compounding. Annualized return adjusts for the actual time invested. For volatile returns, geometric mean is typically lower and more accurate.

Understanding Average Returns

Arithmetic Mean

The arithmetic mean is the simple average of all returns. It adds up all the returns and divides by the number of periods.

Arithmetic Mean = (R1 + R2 + ... + Rn) / n

This measure is easy to understand but doesn't account for compounding effects, which can overestimate actual returns.

Geometric Mean (CAGR)

The geometric mean calculates the compound average growth rate. It's more accurate for investment returns because it accounts for the compounding effect.

Geometric Mean = [(1+R1) × (1+R2) × ... × (1+Rn)]^(1/n) - 1

This is the same as Compound Annual Growth Rate (CAGR) when all periods are equal. It always equals or is less than the arithmetic mean.

Annualized Return

The annualized return converts your total return into an equivalent annual rate, accounting for the actual time invested (years and months).

Annualized Return = [(1 + Total Return)]^(1 / Years) - 1

This metric is especially useful when comparing investments held for different time periods.

Which Measure Should You Use?

  • Arithmetic Mean: Best for predicting future single-period returns or when returns are independent
  • Geometric Mean: Best for measuring past performance and actual growth over multiple periods
  • Annualized Return: Best for comparing investments with different time horizons

Real-World Example

Consider an investment with these annual returns:

Year 1
+20%
Year 2
-10%
Year 3
+15%
  • Arithmetic Mean: (20 - 10 + 15) / 3 = 8.33%
  • Geometric Mean: (1.20 × 0.90 × 1.15)^(1/3) - 1 = 7.29%
  • Actual Result: $10,000 grows to $12,420 (24.2% total)

Notice how the geometric mean (7.29%) more accurately reflects the actual compound growth compared to the arithmetic mean (8.33%).

Important Considerations

  • • Past performance does not guarantee future results
  • • Returns don't include fees, taxes, or transaction costs
  • • Negative returns have a larger impact than positive returns of the same magnitude
  • • More volatile returns lead to larger differences between arithmetic and geometric means
  • • Always consider risk-adjusted returns, not just average returns