# Return

Return is how much money the investment has grown. In other words, it is the value of it today, compared to its value in the past.

As always it is better to use an example when explaining. Consider the following investment, Red and Blue: During the 3 years period (Sep 2009 to Sep 2012), Red grew from £100 to £142, whereas Blue grew from £100 to £184. So Red made £42 and Blue made £84. Red’s return is 42% for 3 years, or 14% per year. Blue’s return is 84% for 3 years, or 28% per year. This 14% and 28% are not accurate, because the return is compounded. The accurate numbers are 12.4% (cube root of 1.42 minus 1) and 22.5% (cube root of 1.84 minus 1).

Return is the most important parameter when considering an investment (the other being the risk). We simply pick the one with the highest return. This sounds very simple, but many people don’t always see it clearly.

That is why it is called “Return on Investment”. It is how much money the investment is making. We have an investment £100 in Red and we get £42. We invest £100 in Blue and get £84.

Let do another example so we really understand the formula. This time the prices don’t start at 100: Red starts from 140 and grew to 182. Blue starts from 120 and grew to 204. The gain is 42 for Red and 84 for Blue, for 3 years. The return for Red is 42/140 = 30%, and for Blue 84/120 = 70%. These 30% and 70% are for 3 years, so per year the return is 10% for Red and 23.3% for Blue. This 10% and 23.3% are not accurate, because the return is compounded, so it is not linear. The accurate numbers are 9.14% (cube root of 1.3 minus 1) and 19.3% (cube root of 1.7 minus 1).

What if it doesn’t cover 3 years duration? Like this: Red covers 3 years (Sep 2009 to Sep 2012) but Blue is only from March 2010 (30 months = 2.5 years).

Return for Red = (180-140)/140 = 40/140 = 28.6% for 3 years. So per year the return is cube root of 1.286 minus 1 = 8.75%.

Return for Blue = (180-120)/120 = 60/120 = 50% for 2.5 years. So per year the return is the 2.5th root of 1.5 minus 1 = 1.5 ^ (1/2.5) – 1 = 17.6%.

So that is how we calculate the return on an investment. This is the number one consideration when investing (in my opinion) so we need to understand it well.

I believe we should learn from actual numbers, not theoretical cases. This is Apple shares, from 18 Sep 2009 to 21 Sep 2012: (source: Google Finance) Apple share price grew from \$185 on 18/9/2009 to \$700 on 21/9/2012.
Return = (\$700-\$185)/\$185 = \$515/\$185 = 278.38% for 3 years = 55.83% per year.

On 23 Sep 2011 the share price was \$404.
Return = (\$700-\$404)/\$404 = \$296/\$404 = 73.3% for 3 years = 20.1% per year.

So the return based on 3 years data is not the same as the return based on 1 year data.

Is 20.1% a good return or not? Yes it is a good return. Generally speaking, for the period Sep 2011 to Sep 2012, return above 10% is a good. Above 20% is very good. How do I know this? By looking at major indexes. An index like FTSE 100 or S&P100.

This is S&P 500 Jun 2011 to Sep 2012: On 21 Sep 2009, S&P 500 was 1460. On 25 Sep 2009, S&P 500 was 1044. The 3Y return therefore is (1460-1044)/1044/3 = 13.3%

On 23 Sep 2011, S&P 500 was 1136. The 1Y return is therefore (1460-1136)/1460/3 = 9.5% FTSE 100 (above) was 5853 on 21/9/12, 5067 on 23/9/11 and 5082 on 25/9/09. In case you are wondering why not all 3 years on 23 Sep, it’s because Google Finance data is on Fridays (weekly data). So the 1Y return is 5.2% and 3Y return is 5.1%.

S&P500 is reflects the growth of the biggest 500 companies in the US. FTSE100 reflects the growth of the biggest 100 companies in the UK. Which is why Apple’s 20.1% return is good. Because it’s higher than the FTSE’s 5% and S&P’s 9%-13%.