The stock market goes up and down. Suppose its level alternates each year between 50 and 100, with no upward or downward trend. What is the capital return on the market?
Common sense suggests the answer is zero. But is that common sense right? In the good years you obtain a return of 100 per cent. In the bad, the yield is minus 50 per cent. The average return is therefore 25 per cent. There is logic to that. If you invested the same amount every year, and sold at the end of a year, you would indeed make – on average – a very attractive return of 25 per cent a year.
What if you bought and sold at random? In that case, four options are equally likely: buy and sell at 50, buy and sell at 100, buy at 50 and sell at 100, buy at 100 and sell at 50. The overall annual expected gain is 12.5 per cent.