
Lots of tricks can be played with
the clever use of percentages. It makes for snappy journalism.
But don't confuse it with analysis. 
Example
If you make 100% one year and lose 50% the next you are back where
you started. {£1,000 plus 100% goes
to £2,000. £2,000 less 50% goes back to 1,000}. The
arithmetical average of your 2 years of returns is 50% (or 25% per
year). Your actual return is zero.
It's the same if you do it the other way round  lose
50% and then make 100%. {£1,000 minus 50% goes to £500.
£500 plus 100% goes back to 1,000}
General Rule
This simple example extends to a more general truth: the arithmetical
average of a series of annual returns is always greater than
the true annual return. For example, five annual returns of +40%,
30%, +35%, +30%, 35% arithmetically average 8% per year, but the
compound annual return is only 2%.
This is particularly useful for misrepresenting
the performance of highly volatile investments:
 "The XYZ Fund lost
50% last year, but this year it's already up 70%". {This
means it is down 15% over two years  100 goes to 50 goes to 85.}
 "The ABC Fund lost 50% in it's first
year but in the next 5 years it averaged 20% a year and never
lost money". {It went 50, 0,0,100,0,0  giving a zero return}
 "The PQR Fund has averaged 20% a year
for five years and only lost money once". {It went +180,
80, 0,0,0  it has actually lost money cumulatively}
Words do bad Maths
Beware the innocent interpretations of journalists.
A fund manager may tell them: "we lost 50% last year but we
are already up 60% in 2003". The journalist may write this
as "XYZ lost 50% last year but has already more than made it
back". But we know that is wrong now, don't we!
Advertising copywriters sometimes make the same
mistake.
Performance Tables
You will sometimes see ranking tables of funds
or fund managers expressed as their average annual outperformance
of a market index. With rare exceptions these will be arithmetic
averages. This is not just because geometric averages are harder
to calculate (although not difficult). It is also because they come
in lower, and it would become more obvious that funds tend to underperform
the market.
