There are two mathematical formulas for analysing investment returns, this article is going to explain the 2 with examples, and discuss how and when they should be used.

Suppose we have an investment vehicle that has annual returns over the past 5 years of 9%, 6%, -5%, 11% and 3% respectively and we want to work out the average annual compound return, the average annual return and then use these to predict future returns. analysing investment returns

The average return is very basic, we just need to find the **arithmetic mean** of the 5 values = (9 + 6 – 5 + 11 + 3) /5 = **4.8%**, but this doesn’t really tell us much as it hasn’t taken into account any compounded growth.

To work out compounded average annual growth we need to use the **geometric mean**. The main benefit to using the geometric mean is the actual amounts invested do not need to be known; the calculation focuses entirely on the return figures themselves and presents an “apples-to-apples” comparison when looking at two investment options over more than one time period.

To work out the geometric mean we multiply each investment return as a percentage and then multiply it by its 1/n root.

It will look like this: analysing investment returns

(1.09 x 1.06 x 0.95 x 1.11 x 1.03) to the power of 1/5 = 1.04546

We need to turn this into a percentage so:

(1.04546 – 1) x 100 = **4.55%**

So what?

Well these figures can be used when estimating future returns of said investment vehicle.

If we are looking for next years expected return, we use the arithmetic mean. So we expect next year for the investment to increase by 4.8%. However if we want to know the expected returns over multiple years then we need to use the geometric mean figure of 4.55%.

The minor difference between the two may not seem much, but compounded over many periods can make a big difference in over all returns. For example.

Let’s say that the investment vehicle is worth $100,000 today and we want to estimate its value in 30 years time when we retire.

Compounded at 4.8% the account is worth $408,167

Compounded at 4.55% the account is worth $379,945

That’s a 7.42% difference