**
What Is the Average Rate of Return?**

When you see the word 'average' return, it's worth checking
how the average was calculated. Here is an example of
two managed funds: Fund A managed by Mr. X, and Fund B
managed by Mr. Y.

Mr. X tells potential investors that he has earned Fund
A investors an 'average return of 20% per year', compared
with Mr. Y whose Fund B earned an average of only 10%
per year. Usually you find the average of a set of different
values by adding up all the values, and dividing that
total by the number of values. This is called the arithmetic
mean. Mr. X's Fund A earned 100% in the first year, but
then lost 60% in the second year. Using this arithmetic
method, we can see that Mr. X can truthfully claim the
average of +100% and –60% is 20%.

Mr. Y's Fund B earned just 10% in the first year, and
earned 10% again the next year. Of course, Mr. Y's arithmetic
average is 10%. An investor who put $100 into the '20%
average' Fund A will see their opening balance of $100
grow to $200 at the end of the first year, only to fall
to $80 at the end of the second year. The investor in
Mr. Y's Fund B sees a much happier picture. Their opening
balance of $100 grew to $110 at the end of the first year,
and rose again to $121 after the second year.

**Check how the average is worked out**

The example shows how the common method for working out
averages, called the arithmetic mean, can present a misleading
picture to investors. You need a better method to find
the average of different rates of return.

One such method is called the geometric mean. Using the
geometric mean:

- Mr. X earned his investors –10.56% per year
and
- Mr. Y earned 10% per year, a much more useful picture
from the investor's point of view.

**How to work out average returns on a computer spreadsheet**

You can work out the geometric mean by using that function
in computer spreadsheet programs, such as Microsoft Excel.
Before you start, beware of keying in percentages. Your
spreadsheet can find it difficult to work with them. The
spreadsheet will refuse to tell you the geometric mean
(or give you a wrong answer), if you key in any negative
percentages. To solve that problem, first turn your percentages
into decimal numbers.

**Turn percentage returns into decimal numbers**

If you are not sure how to do this, here is an example.
If someone asks 'What do you end up with if you invest
$13 and earn 17%?', we find out first that 17% of $13
equals $2.21, and then we add that to $13 to come up with
$15.21.

It would be quicker if we just multiplied $13 by 1.17.
Similarly, if someone asks 'What do you end up with if
you invest $13 but lose 17%?', you could go the long way
round or you just could multiply $13 by 0.83 (1 minus
0.17). Remember a percentage simply divides the number
1 into 100 parts.

To convert your percentages into the right decimal number
for your spreadsheet:

- first turn the percentage rate into a decimal number,
for example 1% equals 0.01, 10% equals 0.10,
- then add that number to 1 if it's a positive return,
or subtract it from 1 if it's a negative return.

Using this method for Mr. X's results, turn his 100%
return into 1 and add it to 1, giving 2. Turn his –60%
into -0.60, which subtracted from 1 equals 0.40. Then
enter 2 and 0.4 into the spreadsheet, avoiding negative
numbers, and get the spreadsheet to work out the geometric
mean.

*By Australian Securities and Investment Commission*