Sherlock Holmes, The Grain of Wheat, and The Snowball

The great fictional detective Sherlock Holmes was a frequent user of cocaine, and his companion Dr. Watson disclosed that the great man preferred a 7% solution, to ease his mind and let him relax to ponder various complex cases. Perhaps slightly obliquely, the phrase “7% solution” immediately made me think of long term investment strategies. A compounded return of some 7% annually (well 7.2%) will see a sum double every ten years, and somewhat strikingly in a period of 100 years, the capital will have grown by over a thousand fold. Quite a “solution”!


This idea of the enormous power of compounding was nicely illustrated by the great Islamic scholar Ibn Kallikan in 1256 (though its origins are almost certainly far older), when he considered the simple task of putting grains of wheat on a chessboard. The puzzle asks you to put one grain of wheat on the first square and double the amount on each subsequent square thereafter…so two grains on square two, four grains on square four etc…until all sixty four squares of the board are covered. So how many grains of wheat will be on the board overall?

Perhaps somewhat astonishingly, on the entire chessboard there would be no less than 18,446,744,073,709,551,615 grains of wheat, weighing about 1,199,000,000,000 metric tons. This is about 1,538 times the global production of wheat (780.8 million tonnes in 2019).

So, doubling is a hugely powerful force, but away from wheat on chessboards, how realistic is this in long-term investment? Interestingly 7% average returns are not that impossible, over many different time horizons global equity markets have delivered those sort of total returns. Detailed information across various asset classes can be found in the Annual Credit Suisse Global Investment Returns Yearbook (see reference below) and for example US equities in real terms (i.e., after inflation) between 1900 and 2019 returned on average 6.5% p.a., and in the last ten years global equites generated 7.6% p.a. (Though it should be noted returns across a wider portfolio of all stock markets for the last 120 years produces a lesser return of 5.2% p.a.) So our desired 7.2% cannot be guaranteed but investment returns can still be a powerful creator of wealth.

Now on to the snowball – this is a simple way to think of the effect of re-investing any investment income – in time it starts to act like a snowball. This analogy was used in a well-known book on the celebrated investor Warren Buffet, The Snowball: Warren Buffett and the Business of Life by Alice Schroeder.

All of these examples point to two simple investment precepts, invest early (or at least regularly throughout your savings life) and always re-invest any income. In forty years at 6.5% p.a. a £1,000 racks up nicely to around £12,500.
Whilst we may not quite get to Holmes’s 7% solution, we will get wealthier and stay somewhat healthier than the great detective.

References

https://www.credit-suisse.com/about-us-news/en/articles/media-releases/credit-suisse-global-investment-returns-yearbook-2020-202002.html