Risk & Measurement

What exactly are we measuring when we call something risky?

Volatility measures dispersion. It is useful, observable and mathematically convenient. But dispersion is not synonymous with the economic consequences an investor experiences. That distinction becomes especially important when return distributions are skewed and the observations furthest from the mean may be the ones the strategy exists to capture.

• Risk Is Not Variance

  The central ATS research programme examining variance, volatility, tail behaviour and the assumptions embedded in conventional performance measurement.

• The Convexity Edge

  Why the shape of returns matters when evaluating strategies designed to participate asymmetrically in uncertainty.

• Two Roads to a High Sharpe

  Why the same conventional return-to-volatility statistic can emerge from very different underlying return structures.

Outlier Evidence

How much of long-run performance is actually carried by the observations we are taught to treat as exceptional?

Outlier Hunting rests on an empirical proposition: financial outcomes are unevenly distributed. A small fraction of observations, trades or markets can account for a remarkable proportion of long-run results. If that is true, portfolio design has to respect it.

• The Lifting Power of Outliers

  An early empirical examination of how disproportionately large observations influence trend-following outcomes.

• The Markets Nobody Chooses

  Evidence for why opportunity can emerge from precisely the markets a concentrated selection process would be tempted to exclude.

• The Death of the Bell Curve

  A data-driven challenge to thin-tailed assumptions and the comfortable geometry of the normal distribution.

• 125 Years of Crisis

  A longer historical perspective on extreme market behaviour and what repeated crises tell us about the distributions investors actually inhabit.

Fractals, Memory & Market Structure

What does the evidence show when we stop assuming that market observations are independent, normally distributed and neatly separated across time?

Fractal market behaviour is not merely a visual metaphor. It raises empirical questions about persistence, memory, scaling, clustering, tails and the way relationships between markets change through time.

The Fractals of Finance research programme examines those propositions across broad futures data rather than treating them as philosophical claims.

• The Fractals of Finance Research Series: The Complete Case

  The consolidated empirical case examining memory, persistence, fat tails, scaling and feedback across sixty-eight global futures markets and more than four decades of data.

• The Fractals of Finance Research Series: Phase 2

  The second phase moves beneath the aggregate statistics to examine changing market states, the balance between trending and oscillating behaviour, coupling, correlation and the structure connecting markets through time.

Compounding & Path

What changes when wealth compounds through time rather than existing as an average on a spreadsheet?

Investment outcomes are multiplicative. The order of gains and losses affects the capital available for what comes next. Drawdowns matter. Survival matters. A strategy can possess an attractive arithmetic expectation and still produce an intolerable path to terminal wealth.

• The Geometry of Wealth

  The major ATS research series on geometric compounding, multiplicative wealth, path dependence and portfolio construction. This is the principal research destination for the subject.

• The Compounder's Delight

  Why apparently similar return statistics can conceal very different journeys to terminal wealth.

• The Fair Game That Kills You

  Why absorbing barriers and multiplicative capital change the meaning of a statistically fair proposition.

• Beyond Expectancy

  Why expectancy alone is insufficient when the sequence of outcomes can determine whether the investor survives to receive it.

Correlation & Diversification

Is diversification merely about smoothing returns, or does it play a deeper role when opportunity itself is uncertain?

For an Outlier Hunter, diversification is not simply a mechanism for reducing measured volatility. It broadens the opportunity set. If the next consequential trend cannot be identified beforehand, excluding markets can mean excluding the very observation that would have mattered most.

• The Hidden Truth of Diversification

  Long-horizon evidence on correlation, portfolio construction and what can disappear when a complex return stream is reduced to a single statistic.

• Diversification for Trend Following Models

  Why seemingly small variations across markets and models can matter to the aggregate portfolio.

• The Dangers of Diversification

  A closer look at the difference between useful breadth and diversification that simply dilutes the objective.

Robustness

What should a trading system be optimised for when the future is not contained in the backtest?

A historical simulation tells us what happened under one realised path. Robustness asks a harder question: whether the underlying logic remains useful when markets, parameters and regimes change.

The objective is not to find the most beautiful solution to yesterday. It is to find machinery capable of remaining serviceable across many possible tomorrows.

• The End of Prediction: Proof from the Data

  Empirical evidence for why universality and adaptability matter more than increasingly precise forecasts of an unknowable future.

• The Trader and the Three Bears

  An earlier treatment of overfitting, underfitting, noise and the difficult middle ground between them.

• The System Anatomy Series

  Where the research consequences become practical architecture: entries, exits, sizing, diversification, execution and the complete systematic programme.

The Research Library

The paths above are curated. They are intended to take a reader to the strongest work first rather than present every article as though each carried equal weight.

The complete archive remains available for readers who want to explore the wider evidence base, earlier investigations and supporting material.