Dealing with Average % in Investment Calculations

 
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Averages – simple, huh?

Investor starts with £100, invests into a fund.

  • Year 1 the fund falls -20%

  • Year 2 the rises +22%

Over the two years what is the average return?

  • -20% +22% = 2% ÷ 2 years = 1%

If the return has averaged 1% over the two years, the investor expects to see £100 x 1%^2, or £102.

The arithmetic is actually £100 x -20%, and then that sum x +22%, so the answer is (100 – 20%) = 80, x 122% = £97.60.

Where did the missing £2.40 go?

Be very wary about advertising and the output of the marketing departments of investment managers, as you can see, it is very easy to mislead investors about past returns.

Like Helvellyn, investing seems quicker coming down than going up.

A very simple rule that is very important – investment returns are not symmetrical; if you have an investment that falls 20%, it has to then grow by 25% just to get back to where you started.

  • Start with £100, fall by 20% down to £80.

  • To get back from £80 to £100 the investment needs to grow by £20, which is 25% of £80.

It’s not a trick, it’s just how maths works. It’s for this reason Charlie Ellis wrote his book on investing called ‘Winning the Loser’s Game’ – the message is that most people would make more money by focusing on not having their investment fall, rather than focusing on the upside.

When is 3% more than 6%?

Take two funds, one whizzy, one plodding

  • Whizzy average over five years is 6% pa

    • +30%, -25%, +35%, -21%, 11%

  • Plodding average over five years is 3% pa

    • +3%, +3%, +3%, +3%, 3%

Which one would you choose?

Which one made more profit?

Whizzy (6% average)

Year 1Year 2Year 3Year 4Year 5
30%-25%35%-21%11%
£100£130.00£97.50£131.25£104.19£115.65

Plodding (6% average)

Year 1Year 2Year 3Year 4Year 5
3%3%3%3%3%
£100£103.00£106.09£109.27£112.55£115.93


 
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