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Triumph of the optimists

22 August 2019

 Salomons Judgement

Why does investing work in the long term? The famous bet by the American economist Paul Samuelson explains it best.

In 1960 Professor Samuelson, teacher at MIT in Cambridge, Massachusetts, proposed the following bet to his colleagues: “I toss a coin. Heads you get 200 dollars, tails you pay me 100 dollars.” A steal of course, but his colleagues refused. Only one of them accepted the bet on the condition that he was allowed to wager a hundred times in a row. Rightly so.

That’s how investing works as well. And you can use it to explain the time needed to do better with stocks than with bonds. It’s a fairly simple sum, with a bit of first-year statistics concerning normal distributions.

Let’s go by the data from Dimson, Marsh and Staunton (2002). The difference in return between stocks and bonds – the excess return – is 4.5 percent. Are you with me? With a volatility (standard deviation) of 13.5 percent, investors have a five-percent chance that bonds will outperform the stock market with 17.7 percent in the first year. Did you get it?

If you like to play with numbers use this equation: 4.5%*t-1.645*13.5%*√t. As the cumulative standard deviation increases with the square root of the investment horizon, the fifth percentile is -22.4 percent in the second year (t=2). But after 25 years, investors can say with a 95-percent certainty that stocks do better than bonds. 

In addition to the volatility, this excess return is important input. The difference between stocks and bonds wasn’t the same in every country in the world. But it is positive in every country. The book by Dimson, Marsh and Staunton is therefore called ‘Triumph of the Optimists’.

The crux is however the investment horizon. The longer it is, the better the outcome and the more optimistic you may be. That’s the true message of Samuelson’s bet.



The author

Roelof Salomons

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