The Vault

THE FRACTALS OF FINANCE | Research Series Phase 2 | Episode 6 of 9

The Fingerprint

The two forces are not symmetric. Positive feedback is gentle and sustained. Negative feedback is intense and brief. The ratio between them is the fingerprint that distinguishes every asset class.

The feedback structure has been described as two forces alternating across time: positive feedback producing trends, negative feedback producing oscillation. Episodes 1 through 5 treated the two forces as roughly equal partners, differing in direction but similar in character. The rolling autocorrelation swings positive, then negative, then positive again.

This is wrong. Or rather, it is incomplete.

When you measure the two forces separately, decomposing the structure into its individual episodes and measuring each one’s duration, volatility, and variance ratio, a finding emerges that changes how you understand every asset class in the universe.

The two forces are not symmetric. In commodity markets, positive-feedback episodes last up to twice as long as negative-feedback episodes. In equities, the two are roughly equal in duration. The asymmetry between the two forces is not a nuance. It is the fingerprint.

The Asymmetry

We segmented the return history of each contract into individual regime episodes, using the rolling ACF sign to classify each day as belonging to a positive-feedback or negative-feedback period. For each episode, we measured its duration in trading days. Then we compared.

Figure 6.1 Duration asymmetry by asset class. Livestock: 2.2x ratio. Grains: 2.0x. Equities: 1.0x. The same structure operates in every class, but the ratio between its two forces varies substantially.

In livestock, a typical positive-feedback episode lasts 189 trading days, approximately nine months. A typical negative-feedback episode lasts 84 days, approximately four months. The ratio is 2.2 to 1. In grains, it is 2.0 to 1. In softs, 1.5 to 1. In fixed income, 1.3 to 1.

In equities, the ratio is 1.0 to 1. Positive and negative feedback episodes last about the same. In FX, it is 0.5 to 1: negative-feedback episodes actually last longer. In energy, 0.6 to 1.

The same structure, operating in every asset class. But the ratio between its two forces varies by a factor of four. That ratio is the fingerprint.

The Puzzle

Episode 4 showed that the variance ratio decomposed cleanly by spectral state: breakout periods produced VR above 1.0, flat periods produced VR below 1.0. That was a universe-level finding. When we break it down by asset class, a richer picture emerges.

Grains spend sixty-eight percent of their time in positive feedback. Livestock spend seventy-six percent. Both should produce full-sample VR above 1.0: more time in the trending state should mean more variance than the random walk predicts.

Figure 6.2 Regime-specific VR by asset class. Livestock shows the largest gap between the two forces (0.709). Equities and energy show inverted patterns where both states produce similar or reversed variance signatures.

Livestock is the clearest case in the universe. Its positive-feedback VR is 1.753: trends persist powerfully, variance grows far faster than linear. Its negative-feedback VR is 1.044, near the random walk. The gap is 0.709, the largest in the universe. Grains show a positive-feedback VR of 1.044 with negative-feedback at 0.990, a modest gap of 0.054.

Positive feedback is gentle and sustained: prices move persistently in one direction, covering more ground than random fluctuations would predict. Negative feedback is intense and brief: prices oscillate back and forth, each move partially reversing the last, covering less ground than expected. The ratio of their intensities determines the full-sample VR, and that ratio is asset-class specific.

Two Kinds of Spectrum

Figure 6.3 Left: equities show both states below 1.0, with a gap of −0.575. Right: grains show positive feedback above 1.0 and negative feedback just below, a much smaller gap. The VR gap is the quantitative fingerprint.

The equity signature is distinctive. Its positive-feedback VR of 0.259 is far below 1.0, meaning that even during periods classified as positive-feedback dominant, equity returns still exhibit the variance signature of oscillation. The equity spectrum does not have a true trending state in the variance ratio sense. It has two flavours of oscillation: mild and strong.

A caveat is necessary. Equity indices are unlike every other contract in this universe. The S&P 500 is a weighted basket of five hundred stocks, and that construction introduces mechanical oscillation that has nothing to do with the feedback structure. Index rebalancing trims winners and adds losers. Cross-sectional averaging dampens variance growth. The deepest options markets create delta-hedging flows that push against price moves. Volatility-targeting funds and pension rebalancers sell into strength and buy into weakness. All of these forces compress the variance ratio below 1.0 at the index level. The honest conclusion is that the equity VR signature is partly a property of index construction, not purely a property of equity price discovery.

This explains why divergent strategies have always been harder in equities than in commodities. It is not just that positive-feedback episodes are shorter. It is that even the positive-feedback periods do not produce the persistent variance that divergent strategies require.

The Map

Figure 6.4 The spectral map. Each class occupies a distinct position defined by its positive-feedback fraction and variance ratio. Equities: lower left. Livestock: upper right. A strategy that ignores this map is ignoring the structure’s instructions.

The spectral map places each class in a two-dimensional space defined by its positive-feedback fraction and variance ratio. The separation is clean. Equities sit alone in the lower left: least positive feedback, lowest VR. Livestock sit alone in the upper right: most positive feedback, highest VR. The remaining classes arrange themselves across the space.

This is not a cosmetic exercise. Each position on the map implies a different optimal approach for divergent and convergent strategies. The lower left demands fast signals, tight stops, and scepticism about trends. The upper right rewards patience, wide stops, and conviction. A strategy that does not calibrate to the map is ignoring the structure’s instructions.

Eight Independent Spectra

Figure 6.5 Regime synchronisation across classes. The eight spectra run largely independently.

The eight spectra run largely independently. The cross-class ACF series show low correlation on average. Equity indices are essentially uncorrelated with every other class. When equities shift toward the oscillating end of their spectrum, it tells you nothing about what grains or metals are doing.

The practical implication is that a multi-asset divergent portfolio diversifies twice. It diversifies across price movements, as conventional portfolio theory describes. And it diversifies across spectral configurations, because the asynchronous timing of regime switches across asset classes means that the portfolio-level spectrum is smoother and more consistent than any individual class’s spectrum.

Not all spectra are equal, and the reader should know where the conviction is strongest and weakest. The feedback structure runs most powerfully in physical commodities: livestock (duration ratio 2.2x, VR gap 0.709), grains (2.0x, 0.054), and softs (1.5x, 0.158). These markets are driven by supply cycles, weather, and biological constraints that create genuine persistence no central bank can suppress. The structure runs most weakly in financial contracts: equities (duration ratio 1.0x) and currencies (0.5x), where intervention, passive flows, and index mechanics compress the signal. Energy sits between the two worlds: a low duration ratio of 0.6x but violent episodic trends driven by geopolitical shocks.

What This Means for Trading

The fingerprint has three direct consequences.

First, parameter selection. The classic approach to trend-following applies a single lookback window uniformly across all markets after normalising position sizes by volatility. This is robust, and it has produced real returns for real investors for real decades. But volatility normalisation equalises the risk. It does not equalise the signal quality. The fingerprint does not argue for abandoning the uniform framework. It argues for calibrating it: tilting an ensemble toward the lookback horizons that match each asset class’s natural frequency.

Second, stop placement. The intensity asymmetry means that negative-feedback episodes in commodities are sharp and brief. Stops that are calibrated to the gentle pace of positive feedback will be triggered by the violence of the reversal.

Third, position sizing. The equity anomaly means that volatility-targeting in equities should not assume the same dynamics as in commodities. Equity positions sized for trending payoffs will be disappointed by the oscillation that occurs even within positive-feedback periods.

The feedback structure persists. The fingerprint varies by asset class. Six episodes of evidence establishing a persistent, asset-class-spanning spectral system of positive and negative feedback. A reasonable person might conclude that trend-following has never had a stronger foundation. Episode 7 tests that conclusion against forty years of actual strategy returns. The result is a paradox that reshapes everything we thought we knew about the relationship between the structure and the profits it can generate.

The structure is intact. The returns are not. Episode 7 explains why, and what comes next.

Endnotes

Methodology

Episode segmentation: each contract’s return series was classified day-by-day into positive feedback (rolling ACF > 0) or negative feedback (rolling ACF < 0) using the nearest rolling window reading (504-day window, 21-day steps). Consecutive days in the same state were grouped into episodes. Episodes shorter than 5 days were excluded. 68 contracts produced sufficient data. Median durations reported to reduce sensitivity to extreme episodes.
Regime-specific VR by asset class: within each asset class, daily returns classified as positive or negative feedback were pooled across contracts. VR(63-day) was computed within each pool. Results: Livestock gap +0.709 (pos=1.753, neg=1.044), Softs gap +0.158 (pos=0.863, neg=0.705), FX gap +0.156 (pos=1.070, neg=0.913), Grains gap +0.054 (pos=1.044, neg=0.990), Metals gap +0.027 (pos=0.917, neg=0.891), Fixed Income gap −0.125 (pos=1.091, neg=1.216), Energy gap −0.470 (pos=1.096, neg=1.566), Equity Index gap −0.575 (pos=0.259, neg=0.833).
Equity positive-feedback VR below 1.0: this finding reflects multiple structural features of equity index construction. Index rebalancing, cross-sectional averaging, delta-hedging by market makers, and systematic rebalancing flows all compress the variance ratio below 1.0 at the index level.
Synchronisation: class-level ACF time series computed as the cross-sectional mean of rolling ACF across contracts within each class, at monthly frequency, from 1996 to 2026. Pearson correlation computed on all 28 off-diagonal pairs.
Positive feedback fraction by asset class: Livestock 75.5%, Grains 68.2%, Softs 61.9%, Fixed Income 54.2%, Metals 54.3%, FX 44.8%, Energy 42.5%, Equity Index 40.9%.

Data and Figures

Same dataset as Episodes 1 through 5. 68 contracts, 8 asset classes.
Figure 6.1: duration asymmetry.
Figure 6.2: regime-specific VR by class.
Figure 6.3: equity vs grains VR comparison.
Figure 6.4: 2D scatter of positive-feedback fraction vs full-sample VR.
Figure 6.5: regime synchronisation heatmap.

This research series is drawn from 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.