The Art of Uncertainty
Following on from David Spiegelhalter's Art of Statistics — a framework for understanding the different types of uncertainty we face as investors, and how to navigate each.
Not all uncertainty is the same
In his Art of Statistics, David Spiegelhalter identifies three fundamentally different types of uncertainty. This distinction is, I believe, one of the most useful frameworks for thinking about investment risk — because each type demands a different response.
Aleatory uncertainty
Uncertainty due to the future being unavoidably unpredictable. A coin is about to be flipped — you cannot know whether it will land heads or tails. This is irreducible randomness. No amount of information can eliminate it.
In investing: the inherent randomness of future market returns, earnings surprises, and macro events. We can describe the distribution of possible outcomes, but we cannot predict which outcome will occur.
Epistemic uncertainty
Uncertainty due to lack of knowledge. The coin has already been flipped — someone knows the result, but you do not. This uncertainty is reducible in principle: with more information, better analysis, or deeper research, you can narrow it.
In investing: gaps in our understanding of a company — hidden liabilities, true normalised earnings, management quality, competitive dynamics. This is the domain where fundamental research adds value.
Ontological uncertainty
Uncertainty about whether our entire conceptualisation is adequate. Our models, assumptions, and mental frameworks themselves may be wrong. The potential outcomes we have imagined, the features we consider important, and the underlying ideas we take for granted — all may be questionable.
In investing: black swan events, paradigm shifts, regulatory regimes we never considered, macro factors we didn’t model. The things we don’t know that we don’t know. This is where humility becomes essential.
The key insight is that each type of uncertainty requires a fundamentally different response. You cannot research your way out of aleatory uncertainty. You cannot diversify away epistemic uncertainty. And you cannot model ontological uncertainty — you can only build resilience against it.
How each type maps to the investment process
Understanding which type of uncertainty you are facing changes how you respond to it.
Addressing aleatory uncertainty: probability distributions
If we don’t have a crystal ball, we can have a stab at the full range of possible outcomes. Using historical distributions, Monte Carlo simulation, and probabilistic thinking, we can describe what we are trying to beat when we buy a stock. The distribution of 3-year equity returns is wide and skewed — understanding its shape is the starting point for realistic expectations and sensible position sizing.
Addressing epistemic uncertainty: research and the 7RQs
Epistemic uncertainty is where fundamental analysis adds the most value. By identifying hidden liabilities, assessing whether profits are inflated, testing for structural threats, and evaluating balance sheet strength, we can reduce the knowledge gap between what we know and what the market knows. This is the domain of the seven red-flag questions — a structured framework for narrowing epistemic uncertainty before committing capital.
Addressing ontological uncertainty: humility and resilience
There will always be things we don’t know that we don’t know. Macro-economic factors which loom larger than our models admit. Regime shifts we never considered. The GFC, the pandemic, geopolitical shocks — these are not events we failed to forecast; they are events whose possibility we failed to adequately conceptualise. The response is not better forecasting — it is building portfolios and processes that are resilient to scenarios we haven’t imagined. This is where diversification, position sizing, stress testing, and scenario thinking earn their keep.
The overconfidence problem
Across all three types of uncertainty, humans share a common failing: overconfidence. We draw our confidence intervals too narrow, we assign probabilities that are too extreme, and we underestimate the range of possible outcomes. Research by Kahneman, Tversky, Tetlock, and Spiegelhalter himself has shown this to be one of the most robust findings in behavioural science.
For investors, this manifests as concentrated positions, insufficient hedging, overreliance on point estimates, and the conviction that we can forecast with precision we do not possess. We systematically underweight ontological uncertainty — the possibility that our entire framework is inadequate.
The calibration test below demonstrates this directly. Provide 90% confidence intervals for 10 factual questions. If you are well-calibrated, you should capture the true answer about 9 times out of 10. Most people capture far fewer.
Calibration Test
How well-calibrated are your beliefs? For each of 10 trivia questions, enter a low and high value representing your 90% confidence interval — the range within which you believe the true answer falls with 90% certainty.
If you are well-calibrated, you should capture the true answer in about 9 out of 10 questions. Most people score far lower, revealing systematic overconfidence.
Risk as a subjective judgement
The final dimension is that risk itself is personal and subjective. It is defined differently by different team members, weighted differently by different investors, and experienced differently depending on your time horizon, mandate, and temperament.
A stock with a wide range of outcomes and negative correlation to the rest of the portfolio might look risky in isolation but contribute to portfolio resilience. A tail event that is negatively correlated with existing positions should give greater consideration to portfolio-level impact than to standalone risk scores.
Communicating views of risk around an investment to colleagues requires acknowledging which types of uncertainty you are dealing with, which you have addressed through analysis, and which remain as irreducible unknowns that must be managed through portfolio construction.
Connecting the threads
The art of uncertainty ties together everything in this research series. Ergodicity shows us that the path matters — aleatory uncertainty compounds multiplicatively. Base rates anchor us in frequencies — addressing epistemic uncertainty through the outside view. Monte Carlo simulation gives us tools to explore the distribution of aleatory outcomes. And ontological uncertainty — the deepest and most humbling kind — is the reason we must build resilience rather than rely on prediction.
Markets would be perfectly efficient if the future were knowable. It is precisely because uncertainty is irreducible — and because most investors respond to it with overconfidence rather than humility — that patient, disciplined, probabilistic investors can earn excess returns. Uncertainty is not the enemy of the value investor. It is the source of the value premium.
Key Takeaway