A Brief History of Probability and Investments

Probability theory was formally developed by French mathematicians Blaise Pascal and Pierre de Fermat who wrote each other a series of letters in 1654 in order to resolve a gambler’s dispute in relation to how to fairly divide a prize pot in a game of chance involving two players finished before either player had won the entire prize pot. The theory that they developed based on expected value had profound implications for a range of different fields including investments, as detailed in the following book:

But how was this probability theory made adaptable to investments? Swiss mathematician Jacob Bernoulli was helpful here as he developed further theory that was published in 1713 based on random experiments e.g. investments with exactly two possible outcomes (e.g. success or failure valued as 1 or 0). If the probabilities of the two outcomes are known, it is possible to determine the distribution of possible outcomes. If there are a series of independent investments and there are a lot of them then the sum of the outcomes can be approximated using the normal distribution, which is very convenient to work with mathematically:

But can we actually determine the probabilities in order to make the mathematics work? This issue was written about by Scottish economist Adam Smith in his famous book The Wealth of Nations published in 1776. Smith acknowledged that in particular cases such as a lottery, the probabilities are known. “Adventure upon all the tickets in the lottery, and you lose for certain; and the greater the number of your tickets [you buy] the nearer you approach to this certainty” Smith wrote. But of course we know that not everyone is rational enough to avoid investing in lottery tickets:

Smith considered more general cases than the lottery but found that, for example, “[t]he probability that any particular person shall ever be qualified for the employment to which he [or she] is educated is very different in different occupations. In the greater part of mechanic trades, success is almost certain; but very uncertain in the liberal professions” including investment professionals! We can calculate our chances of winning the lottery but Smith found that it is not possible to calculate the probability of success in employment or in investments which are uncertain.
This idea was explored further by Frank Knight who in his book Risk, Uncertainty and Profit published in 1921 wrote “[t]he practical difference between the two categories, risk and uncertainty, is that in the former the distribution of the outcome in a group of instances is known (either through calculation a priori or from statistics of past experience), while in the case of uncertainty that is not true, the reason being in general that it is impossible to form a group of instances, because the situation dealt with is in a high degree unique.” One way to think about this is that risk is like picking from a jar when you know what is in it, while uncertainty is like picking from a jar when you don’t know what is in it:

But how do we decide on investments if we can’t always know the probabilities of outcomes? In The General Theory of Employment, Interest and Money published in 1936, John Maynard Keynes wrote: “a large proportion of our positive activities depend on spontaneous optimism rather than on a mathematical expectation, whether moral or hedonistic or economic. Most, probably, of our decisions to do something positive, the full consequences of which will be drawn out over many days to come, can only be taken as a result of animal spirits –

of a spontaneous urge to action rather than inaction, and not as the outcome of a weighted average of quantitative benefits multiplied by quantitative probabilities.”
So it seems that for many investments, knowing the probabilities of outcomes is less of a determinant as to whether we will invest as is whether we are optimistic or pessimistic about the prospects for an investment. And how the investment actually performs will lead our perception of this to change as illustrated by the following example written by Nassim Taleb in The Black Swan: The Impact of the Highly Improbable published in 2007:
“Consider a turkey that is fed every day. Every single feeding will firm up the bird’s belief that it is the general rule of life to be fed every day by friendly members of the human race ‘looking out for its best interests,’ as a politician would say. On the afternoon of the Wednesday before Thanksgiving, something unexpected will happen to the turkey. It will incur a revision of belief.”
At JANA, we employ a range of different approaches to advise clients on prospective investments including deep qualitative research and the very best available quantitative tools included in our Solve software. We’re constantly looking out for investments that are expected to perform well and not end up like the Thanksgiving turkey: