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What's the average rate of return?

Provided by the Austrailian Securities & Investments Commission
A Companion Advisor Article

(Fido is a consumer service offering at the Australian Securities & Investments Commission. This article is reproduced with its permission. We felt the light hearted manor in which it describes the average rate of return question, worthy of inclusion.)

The other day, FIDO read a stockbroker's newsletter discussing rates of return from various investments. The newsletter calculated an 'average return' over a ten year period.

When you see the word 'average' return, it's worth checking how the average was calculated. FIDO found the newsletter used a simple, but potentially misleading, method for averaging the different investment returns.

A tale of two funds

Consider a simple example of two managed funds: the Jumping Fund managed by Mr Hare, and the Plodding Fund managed by Mr Tortoise.

Mr Hare tells potential investors that he has earned Jumping Fund investors an 'average return of 20% per year', compared with Mr Tortoise whose Plodding Fund earned an average of only 10% per year.

Usually you find the average of a set of different values by simply adding up all the values, and dividing that total by the number of values. This is called the arithmetic mean.

Mr Hare's Jumping Fund earned 100% in the first year, but then lost 60% in the second year. Using this arithmetic mean or average, Mr Hare can truthfully claim the average of +100% and –60% is 20%.

Mr Tortoise's Plodding Fund earned just 10% in the first year, and earned 10% again the next year. Of course, Mr Tortoise's arithmetic average is 10%.

Unfortunately, an investor who put $100 into the '20% average' Jumping Fund will see their opening balance of $100 grow to $200 at the end of the first year, only to fall to a dismal $80 at the end of the second year.

The investor in Mr Tortoise's Plodding Fund 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 very misleading picture to investors. You need a much better method to find the average of different rates of return.

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

Mr Hare earned his investors –10.56% per year and
Mr Tortoise 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 a computer spreadsheet programs, such as Excel.

Before you jump in, beware of keying in percentages. Research shows many people find it difficult to work with percentages. Your spreadsheet can also find it difficult to work with percentages. Your 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, draw some comfort from the fact that FIDO can also be a bit slow with numbers.

For example, if someone asks 'What do you end up with if you invest $13 and earn 17%?', FIDO reaches for the calculator and finds out first that 17% of $13 equals $2.21, and then FIDO adds that to $13 to come up with $15.21.

It would be quicker if FIDO 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 Hare'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.

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