Every defined benefit pension scheme has an eighty percent chance of being fully funded ten years from now.

Exactly eighty percent.

Prove me wrong.

That sounds ridiculous, but over the time horizons involved, there is no way of calculating that probability that can be shown to be any more accurate.

So are probabilities really a useful tool for pension funds looking to manage risk and return?

Each decade is a new bag of sweets

Statistics textbooks often talk about taking different coloured sweets out of a bag. If one sweet in every five is green then there’s a one in five chance of picking a green sweet, and so on.

Imagine you’re about to take one sweet out of a bag, and only one. Suppose I tell you there is an eighty percent chance it will be red.

You reach into the bag and take out a yellow sweet. One observation tells us nothing about whether my 80% theory is correct. But before you can take another sweet, someone takes the bag away and replaces it with a different bag. Have I been proved wrong? If the sweet had been red, would I have been proved right?

The fact that you got a yellow sweet out of the first bag tells you very little about the bag it came from, and it tells you literally nothing about the bag that is in front of you now. In just the same way, no vaguely plausible assertion about the next ten years of investment returns can be shown to be more accurate than any other. Each decade is a new bag of sweets.

Will better models help?

Responsible investors want to understand the risks they face. Given what is at stake, people want to calculate the likelihood of success and failure as accurately as possible.

So models have become more sophisticated. Increasing computing power allows us to run increasingly complicated models. Our answers to these questions should be getting more and more accurate.

But we will never know how accurate our models are. Over these sort of timescales, we will never know whether our most gloriously complicated model is any more accurate than just plucking a number out of thin air: we will never have enough data points and the world that we are modelling is ever changing. Probabilities are of very little use as a basis for making long-term decisions.

What does this mean for a long-term investor?

If we cannot accurately estimate probabilities, then we should try to avoid being in a position where those probabilities are important.

Coming back to the bag of sweets analogy, we probably don’t mind not knowing what’s in the bag so long as we don’t have a strong preference for particular types of sweets. But if we really, really hate yellow sweets, or if we’ve bet someone a very large sum of money that the next sweet out of the bag will be red, then we have a problem.

Over the time horizon of a typical pension scheme, risk management is not about trying to understand probabilities. It is about understanding the potential outcomes and the consequences of those outcomes, and designing a strategy such that, where possible, the consequences of each outcome are at least tolerable.

If we can achieve this, then we no longer need to estimate the chances of extreme outcomes, because we are no longer exposed to them.