Probabilistic Frame – The Uncertain System

There are known knowns. These are things we know that we know. There are known unknowns. That is to say, there are things that we know we don't know. But there are also unknown unknowns. There are things we don't know we don't know.

Donald Rumsfeld


All investing is inherently probabilistic, this is something that we know. The interaction of real world and market dynamics creates a system which is inherently uncertain. It can be understood only in terms of expectations and likelihoods, not point solutions.

Learning how to understand these uncertainties has been the aim of probability and statistics. These disciplines provide a framework for our known unknowns. As Peter Bernstein notes in his book, Against the Gods:

“The revolutionary idea that defines the boundary between modern times and the past is the mastery of risk: the notion that the future is more than a whim of the gods and that men and women are not passive before nature.”

But our mastery of risk remains limited. Firstly, whilst these fields have been a huge leap forward in our understanding, for most of us, they are non-intuitive and difficult to grasp. For example, a common adage amongst investors is, “so long as I get more right than I get wrong” – thus demonstrating a basic failure to differentiate the statistical concepts of mode and mean. The Behavioural Frame highlights many other examples of our lack of intuitive skill at probability. As a result, we can often say that probability itself is a known unknown – we know that most people don’t understand it.¹

A second and more intractable issue is our ability to transfer basic statistical theory from an environment of quantifiable risk to unquantifiable uncertainty. In these environments, not only do we not know the outcome, the odds or the payoff, but we usually don’t know what we don’t know about the odds and payoffs. It is in these environments where investors must operate, but where the rules are less clear.

Our Probability Frame therefore has two baskets:

  • Probability and Statistics – Aiming to move basic concepts from the realm of an unknown unknown into that of a known unknown.
  • Uncertainty – How to operate where the odds and payoffs are unknown.
1. Of course, probability can also fall into the realm of an unknown unknown, in the case where we are oblivious to our own lack of understanding of key concepts.