Greg Fisher

Greg FisherGreg FisherGreg Fisher
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Greg Fisher

Greg FisherGreg FisherGreg Fisher
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Complexity in Finance

How can complexity science reshape investment thinking?
In this section, I introduce Complexity Arbitrage — the idea that asset managers can achieve better outcomes by applying concepts from complexity science such as non-ergodicity, systemic risk, price emergence, and adaptive strategy.

Why Complexity Science Matters

Traditional financial models often rest on simplifying assumptions:


  • Equilibrium — markets tend toward a stable state.
     
  • Rational expectations — participants act with perfect information and foresight, and assume everyone shares the same mental model.
     
  • Ergodicity — the average outcome over time matches the average across possible states.
     

In practice, markets are far messier. They are driven by shifting narratives, diverse participants, and constant feedback between expectations and outcomes. The gap between model and market can foster misplaced confidence and poor decisions.

As W. Brian Arthur and colleagues observe, in their Santa Fe Institute Artificial Stock Market paper, “academic theorists and market traders tend to view financial markets in strikingly different ways… The market, in [the] standard theoretical view, is rational, mechanistic, and efficient… From the traders’ viewpoint, the standard academic theory is unrealistic and not borne out by their own perceptions.”


Complexity science helps bridge this gap — recognising patterns, adapting to change, and improving decision-making under uncertainty. The following sections explore the five themes of my Complexity Arbitrage framework.

Complexity Arbitrage

Better investment outcomes come from recognising and adapting to the realities of financial systems — shaped by interaction, feedback, and continual change — rather than relying on static, simplifying assumptions. Complexity science highlights the patterns and processes that capture this dynamism more accurately.


At its core, Complexity Arbitrage brings together five interlinked themes:


  • Emergent Market Prices – values arise from countless interactions, feedback loops, and shifting conditions.
     
  • Narratives – the stories, mental models, and beliefs that shape investor expectations and decisions.
     
  • Modelling – using models as evolving maps of reality, not fixed predictions, and staying open to adaptation.
     
  • Uncertainty – recognising and managing what cannot be predicted or quantified.
     
  • Non‑Ergodicity – understanding how path‑dependence means the journey matters as much as the average outcome.
     

These five themes form the foundation of my Complexity Arbitrage framework, which applies complexity science to improve investment thinking and practice.

The Five Themes of Complexity Arbitrage

Emergent Market Prices

Emergent Market Prices

Emergent Market Prices

Markets in process.

Prices are shaped by countless interactions, feedback loops, and shifting conditions. Seeing prices as emergent — not fixed reflections of “true value” — reveals the underlying processes driving market movements

Narratives

Emergent Market Prices

Emergent Market Prices

The stories we think in. Stories, mental models, and beliefs shape expectations and decisions. Tracking them helps identify sentiment shifts and the potential for self-fulfilling or self-defeating outcomes.

Modelling

Emergent Market Prices

Modelling

Guides, not crystal balls.

Models are crude maps of a patterned reality rather than fixed predictors. Using them adaptively — updating them as conditions change — keeps strategies adaptive and assumptions fresh.

Uncertainty

Non-Ergodicity

Non-Ergodicity

Beyond risk.

Not all unknowns can be measured. Building flexibility into strategies, preparing for varied scenarios, and avoiding overconfidence in forecasts greatly strengthens long-term resilience and strategic adaptability.

Non-Ergodicity

Non-Ergodicity

Non-Ergodicity

 The journey matters.

In non-ergodic systems, the sequence of returns — not just the average — shapes results. Interim losses, volatility, and compounding can leave lasting marks on performance that conventional thinking often overlooks.

Further Reading and Resources

The documents below provide deeper insights into the ideas introduced on this page, grouped into two categories:

 

Complexity Arbitrage Project


  • Complexity Arbitrage Summary – An overview of my approach to applying complexity science in finance, highlighting the five themes and their practical relevance for asset managers.
     
  • Introduction to Complexity Science for Asset Managers – A broader introduction to the foundations of complexity science, written with asset management professionals in mind.
     

Other Resources


  • Complexity Principles – An Introduction to Complex Systems – A primer on the key concepts and characteristics of complex systems, relevant across many domains.
     
  • Complexity Economics – A Summary Paper – An overview of the complexity economics perspective, contrasting it with traditional economic theory.
     
  • PhD Thesis – On the Emergence of Organic Economic Institutions and the Impact of Legal Rules – Doctoral research exploring how economic institutions evolve and the role of legal structures in shaping them.
     

Together, these resources offer both a conceptual grounding in complexity science and a practical framework for applying it to finance, helping asset managers navigate markets with greater insight and adaptability.

Downloads - Complexity Arbitrage Project

Complexity Arbitrage Summary (pdf)Download
Introduction to Complexity Science for Asset Managers (pdf)Download

Downloads - Other Resources

Complexity Principles - An Introduction to Complex Systems (pdf)Download
Complexity Economics - A Summary Paper (pdf)Download
PhD Thesis - On the Emergence of Organic Economic Institutions and the Impact of Legal Rules (pdf)Download

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