# FAQ: the evidence

## I am considering to go for the option to invest in the stock market for my favourite charity. You say on this website that investing in stocks is safe and gives reliable returns historically. What evidence do you have for this?

This section provides more information about the numbers and data that underly the stock market investments option that is a part of the Future Fund. It gives the scientific background to the statements elsewhere on this website that historically investing is safe and gives reliable returns, if two conditions are met: A) you invest with a diversified portfolio (e.g. by investing in the ‘market as a whole’, which means that you invest in all companies that are registered at a stock exchange), and B) you invest with a long investment horizon (‘investment horizon’ means how long you plan to hold the stocks).

The images to the right provide the evidence for this. They were made using the data in this file, which builds on work done by Nobel Prize winning economist Robert R. Shiller and a file produced by Yale University.

The images show the average annual return that you would have had if you invested in the market as a whole. Each image shows this for a different set of investment periods (the ‘investment period’ is how long you have actually held the stocks, if the period is in the past):

1. Figure 1 for invesment periods of 1, 2 and 5 years

2. Figure 2 for periods of 5, 10 and 25 years

3. Figure 3 for periods of 25, 50 and 100 years

The lines are split into three graphs, as opposed to putting them all in one graph, to improve the visualization. ‘5 years’ and ’25 years’ are both in two graphs on purpose – we’ll get to that later.

The first thing to note from these three graphs is their x-axes. They all start in 1871. This is because from this year onwards, we have good stock data available. The lines are ‘rolling averages’, meaning that every month a new average was calculated for the 1, 2, 5, 10, 25, 50 or 100 years preceding it. That is why the larger the investment period, the later the line starts in the graph. The graphs include analysis of 1794 months in total between january 1871 and june 2020.

Secondly, note that the average annual interest from 1871 to 2020 is 6.93%. Again, this is ‘real return’, meaning it is already corrected for inflation. The average uncorrected return is higher, around 9%.

Thirdly, note that as the investment period gets bigger, the variance (‘variance’ means how much the line deviates from its average) around the average interest gets smaller (notice how different the y-axes are in the 3 graphs). If you invested for 1 year, if you started in precisely the right month, you would have made an interest of 151.3% (!). If you started in the worst month, you would have made -58.1% (meaning you lost 58.1% per year). Depending on the month and year in which you started to invest, you could get really lucky or unlucky. However, as the investment period grows, these numbers get smaller. With 5 years they are already 33.3% and -13.2%, with 10 years 20.0% and -5.9%, and so on.

Source for this and the following two graphs: data build upon Robert R. Shiller, Stock Market Data Used in “Irrational Exuberance” Princeton University Press, 2000, 2005, 2015, updated data, available from the Department of Economics at Yale university. The Future Fund’s adaptations can be downloaded here.

This is why ‘5 years’ and ’25 years’ are both in two graphs: to visualize the decrease in the variance as the investment period gets bigger. The line with the smallest variance in the first graph (investment period of 5 years) is the same as the the line in the second graph with the largest variance! And this goes the same for the line with the smallest variance in the second graph (investment period of 25 years): it is the same as the line with the highest variance in the third graph. This shows the big differences between the variance for small and long investment periods. So the conclusion from all this is: the longer the investment period, the smaller the variance around the average interest.

Another way to visualize this is to take these best and worst average annual interests in history for each investment period. When you do that, you get the bar chart at the bottom of this section.

Note that there has not been a single (!) investment period of 25 years since 1871 — out of 1794 periods that were analysed, each starting in a different month — during which the average real return per year on the stock market as a whole was less than 0. This also matches with the line graph for this investment period above – it never dips below 0. If you had huge bad luck and you started investing in the worst month, you still had a positive return every year of 2.1% on average. If you were lucky, and you started out in the best possible year, you achieved a return every year of 12.4% on average.

So, the conclusion of all this data is: as long as you invest as diversified as possible (in the market as a whole) and have an investment horizon of more than 25 years, historically, investing in stocks is safe and gives an average return of 6.9% per year on average. The same calculations can be done for regular savings, this is also safe historically, but gives only an average return of 2.3% per year.

**Note that for 25-, 50- and 100-year investment periods, regardless of the month and year in which you started to invest, the average annual return was ALWAYS positive.** Source: Data build upon Robert R. Shiller, Stock Market Data Used in “Irrational Exuberance” Princeton University Press, 2000, 2005, 2015, updated data, available from the Department of Economics at Yale university. The Future Fund’s adaptations can be downloaded here.