Market Geometry

What shape is the market in?

Topology-family measures computed daily, one asset class at a time — mixing bonds and the dollar into an equity cloud reads flight-to-quality as "structure", so each group gets its own gauges and its own tree. The TDA gauge (persistent homology) asks whether the geometry of a group's dynamics is deforming; the market tree (minimum spanning tree) shows its correlation skeleton and warns when it collapses toward a single hub. Each group shows one verdict, from the one signal that survived its own audit — with the historical odds attached, so a reading translates into an expectation. Full evidence in the audit.
How to read this page — start here

What the TDA gauge measures, in plain words. Take the last 60 trading days. Each day is a dot, positioned by how every market in the group moved that day — 12 markets means each dot lives in 12 dimensions. In a normal market those 60 dots form a shapeless fuzz: days don't relate to each other in any persistent way. When markets start moving in coordinated, repeating patterns — the kind of synchronised behaviour that builds before selloffs — the dot-cloud develops actual shape: loops and strands that persist. The TDA gauge is simply "how much shape does the cloud have right now", scored against the group's own last five years.

Direction: high = warning, low = normal. There is no good high reading.

VerdictWhat it meansWhat happened historically (next 60 days)
quiet The cloud is shapeless — no unusual coordination. Baseline odds: a >5% drawdown followed only ~17–20% of the time. Nothing to act on here.
watch Structure building (above the 70th percentile), but below the audited alert line. In-between zone — check the stress gauges more often.
alert Heavy structure (>90th percentile) while turbulence still reads calm — coordination building under a quiet surface. This is the audited configuration. A >5% drawdown followed 44–48% of the time (2–3× baseline) and volatility ran ~30% higher — expect a turbulent market even though today looks calm.
hot Geometry hot, but turbulence is also elevated — the storm is already visible. The stress gauges cover this case; geometry adds little once stress is overt.

The commodities panel uses a different signal — hub concentration. The market tree below shows which markets are correlated to which; normally commodities trade on their own drivers (gold on rates, oil on supply). When the tree collapses so that everything connects through one hub, the group has become a single bet — and historically a >10% commodity drawdown followed 44% of the time vs 15% from distributed readings. Same direction: high concentration = warning.

Tree length (bottom chart) is context, not a signal: shorter = markets more correlated = less diversification inside the group. Its information overlaps the absorption ratio, so we don't issue verdicts from it.

All the odds above come from the audit on this page — ~12 independent episodes over 16 years, so treat them as odds-shifters, not certainties. One sentence to take away: high geometry reading + calm surface = the historical setup for rough markets; everything else here is context.

The market tree — correlation MST, trailing 90 days
TDA landscape norm — persistent H1 structure of the 60-day return cloud
shaded bands: the worst cross-asset drawdown episodes in the sample
Tree length — mean MST edge distance (contracts in stress)
lower = the group more unified = less diversification inside it

The audit that earned this page

We don't add indicators because they're fashionable — every tool has to beat the incumbents somewhere, out loud. The original audit ran on 9 markets; when the board expanded to 20 in July 2026, the whole study was re-run on the full 18-market cross-asset panel against the site's existing fragility gauges, Turbulence and the Absorption Ratio. Trailing percentiles only, no look-ahead, results published win or lose. The per-class views above use the same machinery; the audited evidence below is from the cross-asset panels.

Did it warn before the worst drawdowns?

EpisodeDepthTDA 60d beforeTDA 20d beforeTurbulence 20d beforeAbsorption 20d before
2015–16 global−23%p45p83p83p17
2018−13%p17p34p22p20
COVID 2020−28%p77p0p27p55
2022−15%p67p66p70p24

Episodic, not universal: the TDA gauge built into 2015–16 and flickered before COVID; nothing warned before 2018 — which is exactly why this page sits alongside Systemic Risk rather than replacing it.

Does it add anything the incumbents don't have?

The decisive test, per panel: when a group's headline signal is hot (>90th percentile) while that group's Turbulence reads calm (<70th) — the configuration the incumbents call safe — what actually happened over the next 60 days?

Panel · signalP(>5% dd) hotquietP(>10% dd) hotquietFwd 60d vol hotquiet
Equities · TDA44%20%16%6%12.3%9.6%
Cross-asset · TDA48%17%11%5%11.1%8.1%
Commodities · hub concentration67%39%44%15%

Those three pairs are the page's headline verdicts — each panel shows only the signal that passed its own audit. The failures are listed too: commodity TDA carries no drawdown information (hot and quiet readings led to identical outcomes); equity hub concentration is mildly inverted; tree tightness everywhere overlaps the absorption ratio and is shown as structure only.

A retraction. An earlier version of this page reported cross-asset hub concentration preceding ~2× worse drawdowns. After a calendar data-quality fix (mixed Sun–Thu/Mon–Fri trading weeks had been deleting whole days from the panel), that result does not replicate and is withdrawn. The hub-collapse signal is real only within commodities. We leave this note here because silently deleting findings is how quant marketing works, and this page isn't that.

Honest limits

A handful of episodes is still a small sample — a conservative block bootstrap puts these spreads at p≈0.10–0.16, so treat them as odds-shifters, not certainties. Parameters follow the literature (60-day windows per Gidea & Katz; 90-day correlations per the MST literature) with no optimisation. These are environment measures: they say a group's geometry is deforming, not that a crash is scheduled. Treat readings as a prompt to check the regime board and stress gauges, never as a standalone signal.

Methodology

TDA landscape norm. For each asset class, each day, we take the trailing 60 daily return vectors of the group's markets — a cloud of 60 points — and compute its Vietoris–Rips persistent homology (H1: loops). The persistence landscape's L1 norm summarises how much robust geometric structure the cloud contains. Markets are scaled once by full-sample volatility so no single asset dominates; day-to-day volatility structure is deliberately preserved — it is part of the signal. Smoothed over 10 days; dials show the trailing 5-year percentile within the group's own history. After Gidea & Katz (2018), "Topological data analysis of financial time series: Landscapes of crashes."

Market tree. From each group's trailing 90-day correlation matrix we build Mantegna's distance d = √(2(1−ρ)) and extract the minimum spanning tree — the shortest network connecting the group's markets. Its mean edge length contracts when correlations rise; its shape shows which markets carry the connections; its collapse toward a single hub is the configuration the audit flags. After Mantegna (1999) and Onnela et al. (2003).

Groups: Equities (12 indices), Commodities (gold, silver, WTI, copper), Cross-asset (all 18 — adds US 10Y Treasuries and the Dollar Index; interpret with care, since safe-haven flows read as unification there). Crypto is excluded: 24/7 calendars distort a daily-close panel. Rates and FX are too few for their own tree. All series precomputed in the daily pipeline. Educational, not investment advice — see the Disclaimer.

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