I joined Niels Kaastrup-Larsen on Episode 391 of the Systematic Investor Series to walk through the empirical research behind The Fractals of Finance. What follows is a summary of the conversation, from the crude oil shock that opened proceedings to the three lines of evidence that make the case for feedback as the structural foundation of financial markets.
Opening with crude oil
We started, as Niels and I often do, with what had been on our radar. For me that was the crude oil move of the past few weeks. WTI had drifted steadily lower from around $87 to roughly $66 over eighteen months, an orderly uneventful decline with stabilising forces firmly in control. Then in a very short timeframe it spiked to around $119 before reversing sharply to about $84 by March 10. An 80% move followed almost immediately by a 30% reversal.
My interest was not primarily in the geopolitical story, though I am not dismissing the genuine supply risk involved. What caught my attention was what the market’s reaction itself was telling us about the state of the system when the shock arrived. When you have eighteen months of compressed volatility, heavy short positioning, and amplifying participants largely absent from the market, you have a system that is structurally loaded. The geopolitical event was the ignition. The fuel had been building for over a year.
"It's exactly what a market looks like when lightning hits dry undergrowth. The undergrowth here was the setup. All it needed was a catalyst."
Niels added an important dimension here, noting that roughly 20 million barrels per day are currently trapped in the Hormuz Strait region, equivalent to the demand destruction seen when the entire world shut down during the pandemic. The storage implications alone carry significant second and third order effects. We also touched on the inflation transmission channel: oil flows through transport, manufacturing, food production, and eventually wages and central bank policy. The asymmetry matters too. Prices in the real economy go up fast and come down slowly, so the inflationary impulse tends to linger well after the commodity price has pulled back.
As trend followers, Niels and I agreed that we do not need to call which scenario plays out. We stay positioned and let the market tell us.
The logical test at the heart of the research
Moving into the main research, I started with a logical test rather than a statistical one. In a world where markets had no memory at all, three things would have to be true: trends could not persist, returns would follow a normal bell curve, and volatility would be steady and predictable. Those are not opinions. They are the mathematical consequences of a world without feedback. So I turned the question around. If all three of those predictions are violated simultaneously, in every market we can study, then the conclusion is inescapable: feedback is the fundamental structural property of financial markets, not a feature of particular periods or asset classes.
Signature one: structural memory
The first measurement was whether markets carry memory in their structure. The tool for this is the Hurst exponent, a number between zero and one. A score of 0.5 is consistent with pure randomness. Above 0.5 indicates long-range dependence.
It is worth being precise about what this measures, because Niels raised exactly the right question about it. The Hurst exponent is not saying that because the market went up today it is more likely to go up tomorrow. That kind of simple day-to-day directional persistence effectively averages to zero over large samples, which I will cover in more depth in a future episode. What the Hurst exponent captures is something deeper: whether the magnitude and clustering of moves, the way large moves follow large moves and quiet periods follow quiet periods, exhibits a kind of memory that a purely random process would not produce. As I put it in the conversation, it is the explosive volatility out of a calm compressed state that trend following is actually exploiting, not day-to-day directional autocorrelation.
The mean Hurst exponent across all 68 markets was 0.866. Not in some markets or some periods. Every single one, every decade. Decade averages ranged from 0.707 to 0.757 through financial crises and regime changes. That structural memory was always there.
Signature two: fat tails
Under the standard bell curve model, a five-sigma event should occur roughly once every three and a half million trading days. We have not accumulated three and a half million trading days in the entire history of liquid financial markets. We should essentially never see one.
In the dataset, five-sigma events occurred 5,791 times more frequently than the standard model predicts. Nearly six thousand times more frequent, across all eight asset classes. The tails follow a power law with an exponent of approximately 3.33, which Niels asked me to explain. The short version is that 3.33 pushes us firmly into leptokurtic territory: tall narrow peak, heavy tails, and a distribution that is definitively not a bell curve in any liquid market we assessed. The practical consequence is that any risk model built on bell curve assumptions is not slightly underestimating the probability of large losses. It is underestimating it by orders of magnitude.
Niels connected this directly to DUNN’s use of dynamic position sizing rather than volatility targeting, and the distinction is exactly right. Targeting a fixed volatility level implicitly assumes recent volatility guides future move size, which works reasonably well for the middle of the distribution but leaves you completely unprepared for the tails. Sizing for the calm of $66–$80 range-bound crude and then experiencing a move to $119 is not bad luck. It is the predictable consequence of using a bell curve tool to manage a power law risk.
Signature three: volatility clustering
The third signature is the tendency for turbulent periods to bunch together. We measured this using the autocorrelation of the size of daily moves across all 68 markets. The average was 0.353. That is a strong, consistent signal that volatility has memory, not just direction.
With all three in place, the picture is complete. Every prediction of the no-feedback world is false, in 68 out of 68 markets, across eight asset classes, across four decades.
Two types of participant, one distribution shape
There is something more interesting to say about what the distribution itself is telling us. The distinctive shape, tall narrow peak and heavy tails, is the signature of a market running two distinct participant types simultaneously. Convergent participants push back against moves away from where they think prices should be. They produce the tall peak, because most of the time they dominate. Divergent participants push in the direction the market is already moving. Trend followers, momentum traders, stop-loss orders, margin calls. They produce the fat tails, because periodically their collective behaviour overwhelms the stabilising forces.
As Niels noted, at DUNN they are often actually selling oil as the price spikes, reducing exposure within their risk framework. So divergent participants are not always amplifying in one direction at all times. The dynamics are more nuanced than a simple amplifier label suggests, which is part of why the distribution looks the way it does.
The phase transition
The agent-based simulation that formed the final part of the research found a threshold at roughly 25 to 30 percent divergent participation, below which the market is stable and bell curve-like, and above which persistent trends, volatility clustering, and fat tails all emerge simultaneously. The transition is sharp, not gradual. The real markets in the study appear to operate above that threshold, which is why we see those three signatures so consistently.
This reframes regime changes. They are not random weather. They reflect shifts in the balance between stabilising and amplifying participation, driven by observable conditions: volatility, positioning, fear, momentum, margin levels. A quiet market is not broken. It is operating below the threshold. A sudden directional move is not anomalous. It is exactly what a system above the threshold does.
"Every market, all the time, is in some state of accumulated potential. Our job as systematic traders is not to predict when the lightning will arrive. It is to be positioned to participate when it does."
The broader conversation
Niels brought several things to the conversation that extended it beyond the research itself. He noted that the SocGen Trend Following Index had just hit a new all-time high at the end of February, while the short-term traders index was still only about 50% recovered from its drawdown. The longer-term strategy was doing exactly what the research would predict during a period of fat-tail market behaviour.
He also raised the interest rate cycle question: if we have just turned from 40 years of lower lows in rates to higher highs, the regime shift may have decades to run. Most investors anchored by recency bias will keep expecting a return to what they just experienced. Trend following, being rules-based and patient, simply does not have that bias. The models wait. As Niels put it, even through periods that were not conducive to trend following, the strategy still made money, just not as much as expected. That robustness across regimes is precisely what the research explains structurally.
Niels closed by calling the book “Michael Lewis meets Mandelbrot,” which I will take.
Listen to the episode.
Why Trend Following Works… the Evidence ft. Richard Brennan
Want the theoretical foundation for why trend following works?
The Fractals of Finance: Determinism, Adaptation and the Geometry of Markets
The book explores the full architecture of feedback, fat tails, and fractal structure in financial markets, and what it means for how we trade, invest, and understand risk.
Available now on Amazon in paperback, hardcover, and Kindle.
Want a practical field manual for trading trends and capturing outliers?
The Aussie Turtles Trend Following Guide: A Field Manual for Hunting Outliers adapts the timeless principles of the original Turtle traders into a systematic, rules-based approach for modern markets. Co-authored with Adam Havryliv.
Available now on Amazon in paperback, hardcover, and Kindle.