Geometric Mean Return Calculator

Formula

To calculate the Geometric Mean Return (R_g):

\[ R_g = \left( \frac{EV}{BV} \right)^{\frac{1}{n}} - 1 \]

Where:

$ R_g $ is the geometric mean return
$ EV $ is the ending value
$ BV $ is the beginning value
$ n $ is the number of periods

What is Geometric Mean Return?

The geometric mean return is a measure of the average rate of return of an investment over multiple periods, taking into account the compounding effect. Unlike the arithmetic mean, which simply averages the returns, the geometric mean return provides a more accurate representation of the investment's performance by considering the cumulative effect of gains and losses over time. This makes it particularly useful for evaluating investments that experience volatility or varying rates of return across different periods.

Example Calculation

Let's assume the following values:

Ending Value $ EV $ = $1500
Beginning Value $ BV $ = $1000
Number of Periods $ n $ = 3

Step 1: Divide the ending value by the beginning value:

\[ \frac{EV}{BV} = \frac{1500}{1000} = 1.5 \]

Step 2: Take the nth root of the result:

\[ \left(1.5\right)^{\frac{1}{3}} \approx 1.1447 \]

Step 3: Subtract 1:

\[ 1.1447 - 1 = 0.1447 \]

The Geometric Mean Return is approximately 14.47%.