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Calculate The Geometric Mean Return of The Following Data Set

Reviewed by Calculator Editorial Team

The geometric mean return is a financial metric that calculates the average rate of return over a specified period for an investment, taking into account the compounding effect of returns. Unlike arithmetic mean, which simply averages the returns, geometric mean provides a more accurate representation of growth when returns are compounded.

What is geometric mean return?

The geometric mean return is a compounded annual growth rate (CAGR) that accounts for the time value of money. It's particularly useful for comparing investment performance over different periods or for investments that compound returns.

Key characteristics of geometric mean return:

  • Accounts for compounding effects
  • Provides a more accurate measure of investment growth
  • Useful for comparing investments with different holding periods
  • Can be negative if the investment loses value

How to calculate geometric mean return

To calculate the geometric mean return, you'll need:

  1. A series of periodic returns (typically annual)
  2. The number of periods in your data set

The calculation involves:

  1. Converting each return to its growth factor (1 + return)
  2. Multiplying all growth factors together
  3. Taking the nth root of the product (where n is the number of periods)
  4. Subtracting 1 to get the geometric mean return

Formula

Geometric Mean Return Formula

GMR = (∏(1 + ri))^(1/n) - 1

Where:

  • GMR = Geometric Mean Return
  • ri = Individual period returns
  • n = Number of periods

The formula calculates the compounded growth rate that would produce the same final value as the sequence of individual returns.

Example calculation

Consider an investment with the following annual returns: 10%, -5%, and 15%.

  1. Convert each return to growth factor:
    • 1 + 10% = 1.10
    • 1 - 5% = 0.95
    • 1 + 15% = 1.15
  2. Multiply the growth factors: 1.10 × 0.95 × 1.15 = 1.1975
  3. Take the cube root (since n=3): 1.1975^(1/3) ≈ 1.0616
  4. Subtract 1: 1.0616 - 1 = 0.0616 or 6.16%

The geometric mean return is approximately 6.16%.

Interpreting results

A positive geometric mean return indicates that the investment has grown over time, while a negative value indicates a decline. The result is typically expressed as a percentage.

Key considerations:

  • Geometric mean is more appropriate than arithmetic mean for investments that compound
  • It provides a fair comparison between investments with different holding periods
  • The result is sensitive to negative returns, which can significantly impact the overall result

Note

For investments with frequent compounding periods (like daily returns), you should adjust the calculation accordingly. The example above assumes annual returns.

FAQ

What's the difference between geometric and arithmetic mean return?

Arithmetic mean simply averages the returns, while geometric mean accounts for compounding. Geometric mean provides a more accurate representation of investment growth.

When should I use geometric mean return?

Use geometric mean when comparing investments with different holding periods or when returns are compounded. It's particularly useful for long-term investment analysis.

Can geometric mean return be negative?

Yes, if the investment loses value over time, the geometric mean return will be negative. This indicates overall decline rather than growth.