Average Return Calculator

Calculate arithmetic mean, geometric mean (CAGR), and total growth from annual returns

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Geometric Mean (CAGR)

About the Average Return Calculator

Our average return calculator computes both the arithmetic mean and geometric mean (CAGR) of a series of annual returns. While the arithmetic mean gives a simple average, the geometric mean reflects the true compounded growth rate of your portfolio over time.

Understanding the difference between arithmetic and geometric returns is crucial for accurate investment analysis. Many investors mistakenly use the arithmetic mean to project future portfolio values, which overstates expected returns. The geometric mean, or CAGR, tells you what you actually earned year over year.

Use this calculator to analyze your portfolio's historical performance or to evaluate potential investments. Enter up to five years of returns to see both averages, along with the total growth and what a $10,000 initial investment would have grown to over the period.

How to Use This Calculator

  1. Enter the annual return percentage for each year (up to 5 years). Negative returns are allowed.
  2. Enter at least 2 years of returns for meaningful results.
  3. Click Calculate to see the arithmetic mean, geometric mean (CAGR), and total growth.

The Formula

The arithmetic mean is the sum of returns divided by the number of periods. The geometric mean (CAGR) is the nth root of the product of (1 + each return) minus 1.

Arithmetic Mean = Σr / n   Geometric Mean = (Π(1+r))^(1/n) - 1

Frequently Asked Questions

Why is the geometric mean lower than the arithmetic mean?

Geometric mean is always less than or equal to the arithmetic mean due to the effect of volatility. Large negative returns have a disproportionate impact on compounded growth, which the geometric mean captures but the arithmetic mean does not.

Which average should I use for investment returns?

Use the geometric mean (CAGR) to measure your actual investment performance over time. The arithmetic mean is useful for estimating expected returns in a single period but overstates long-term compounded growth.

Can the geometric mean be negative?

Yes, if the overall investment lost value over the period, the geometric mean (CAGR) will be negative. This reflects the true compounded loss rate, unlike the arithmetic mean which may still show a positive average even with some losing years.

How many years of data do I need for meaningful results?

At least 3-5 years of returns are recommended for meaningful average return calculations. Longer periods of 10+ years provide more reliable estimates of a strategy's long-term expected return.

What is the impact of volatility on geometric mean?

Higher volatility reduces the geometric mean relative to the arithmetic mean. This is known as volatility drag. The larger the year-to-year swings in returns, the bigger the gap between the arithmetic and geometric averages.

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