Make sure you have understood 'interest'.

Income return

If you deposit £100 for a year at 3% interest you will get £103 back. This is your £100 deposit (' principal') and £3 of interest ('income').

You might look on the £100 as an investment - putting money away to get more back in the future. The £3 could then be called the 'return on the investment', or, in short, a '3% return'. It is also called a '3% income return'.

Capital return

If you buy a gold coin for £100 and sell it a year later for £103 you have again made a 3% return. This time you have made this money through capital appreciation. So it is called a 'capital return'. But it's £3 just the same.

Total return

If you invest £100 in a share and it pays a dividend of £3 and also goes up in value to £102 you have made a total of £5. Cleverly, this is called the 'total return', or just 'return'. As an investor, you do not care about the separate capital and income returns (except for tax reasons). You just care about your total return.

Get used to adding your income return (or 'interest' or 'yield' or 'dividend') to your capital return (or 'capital gain') to get your total return. In the example, 3% + 2% = 5% total return.

Multi-year returns

Skip this section on first reading if you like.

If you invest £100 and get a capital return of 5% you have £105 at the end of the year. If your investment then earns 10% it adds £10.5 to go to £115.50 in year 2, . Your total return over two years is 15.5%.

There's a way of reducing this information to a single 'annualised return' or 'annual return'. In this example you have made a return of 15.5% over 2 years. What is the annual return which, compounded over two years, would deliver 15.5% and thus deserve to be called the annual return for this particular investment?

• not 7.5%, which would be the average of 5% and 10% -

• ……. or 7.75%, which is half of 15.5% and would be simple interest -

• ……. but 7.47% - or ‘7.47% per annum compounded’.

You would refer to your investment as making an 'annual return of 7.47%'.

These differences look trivial, and for one year they are. But the miracle of compounding builds up the differences over the years to make these small annual differences important. If you chose bigger numbers, or mix positive and negative returns, the difference becomes even more striking.

If you want to understand the maths (which is not necessary) glance at Compounding Effect.

It is possible to calculate an annual return from any old mish-mash of cash flows over any period. The 'annual return' for this mish-mash is sometimes called the 'Internal Rate of Return (IRR)'. But you should just call it ‘return’.

For clarity there must be a reference period. This could be ‘short-term return’ or ‘long-term return’ or ‘10-year return’ or ‘historical return’;

All other things being equal, you want the highest possible returns from your investments.

Return games

If you’ve got this far, it’s worth warning you of a popular way of funds or pundits misrepresenting their achievements.

In the example above the IRR (7.47%) is less than the average of the two yearly returns (7.5%). As a mathematical truth this is always the case. The average of the annual is always more than the annual!

And it gets worse: the more volatile the figures, the larger the discrepancy.

Suppose a fund doubles and then halves. It gets back to where it started. Year 1: +100%. Year 2: -50%. Annual return: 0%. Average annual return: (100-50)/2= 25%

Suppose a fund quadruples (goes from 100 to 400) and then loses 75%. It also gets back to where it started. Annual return: 0%. Average annual return: (300-50)/2= 125%

Fund 1 will promote itself as ‘achieving average annual returns of 25%’ and Fund 2 will promote itself as ‘achieving average annual returns of 125%’. Both totally misrepresent the breakeven position. Worse, choosing between the two you would be persuaded to pick Fund 2 when in fact what you should do is pick fund 1 because it is less volatile (though pretty horrific in that department).

This example explains the important general principle. Average annual returns are inflated by volatility. and you don’t want volatility.