# How to Compute Geometric Mean Return

Geometric Mean Return Calculator
Value at beginning of Year 1:
\$

Value at end of Year N, and number of years:
\$            N =

In business and statistics, the geometric mean return (sometimes called the geometric average return) is the yearly rate of return averaged over a fixed period of time. If you have an asset that appreciates in value every year, the geometric mean return tells you the equivalent annual interest rate that will yield the same return.

You can compute the GMR if you know the value of the asset at the end of each year, or you simply use the initial value and ending values to calculate GMR. The article below will explain the math, or you can use the convenient geometric average return calculator on the left.

### Method 1: Using the Asset's Values During Each Year

We motivate this method by example. Suppose you buy a piece of property for \$100, and the appreciated yearly values are given in the table below:

 End of Year 1 Value = \$120 (% increase = 20%) End of Year 2 Value = \$150 (% increase = 25%) End of Year 3 Value = \$168 (% increase = 12%) End of Year 4 Value = \$196 (% increase = 16.667%)

Each year the value increases, but not by a constant percentage rate. To find the average percent increase over the 4years, i.e., the geometric mean return, we calculate

[(1.20)(1.25)(1.12)(1.16667)]1/4 - 1
= 1.1832 - 1
= 0.1832, or 18.32%

So the value increases by an average of 18.32% each year. The next method shows an equivalent and more efficient way to calculate the mean yearly return.

### Method 2: Using the Asset's Starting and Ending Values

If the starting value is \$100 and the ending value is \$196, then we can compute the geometric mean return more efficiently with this calculation

(196/100)1/4 - 1 = 1.1832 - 1 = 0.1832 or 18.32%

which gives the same answer as before. The general formula is

(Value end ÷ Value start)1/N

Where Value start is the initial cost or worth of the item, Value end is the value at the end of the period, and N is the number of years.