# GEOMETRIC AVERAGE EXPLAINED

In the world of investments, an arithmetic average (the sum of a series of numbers divided by the count of that series of numbers) is not always appropriate.

Let’s imagine you have invested in the stock market for five years, and your returns each year were 90%, 10%, 20%, 30% and -90%. Your arithmetic average return over this period would be 12% [(90+10+20+30-90)/5].

However, when it comes to annual investment returns, these numbers are not independent of each other. If you lose money in one year, you have less capital to generate returns the following year, and vice versa. Therefore the geometric average of your investment returns will provide a more accurate picture.

To do this, we simply add one to each number (to avoid any problems with negative percentages). Then, multiply all the numbers together, and raise their product to the power of one divided by the count of the numbers in the series. Take the answer and subtract 1.

In this example, it would be calculated as follows: [(1.9 x 1.1 x 1.2 x 1.3 x 0.1) ^ 1/5] - 1. This equals a geometric average annual return of -20.08% − substantially below the 12% arithmetic average.