Terrain and fragility: two readings beneath the index

Two questions define the terrain

How strongly is uncertainty being priced, and how collectively are names repricing?

Constituent IV stress is each name's 30-day implied volatility ranked against its own prior history, weighted across the basket by index weight. Synchronisation is the trailing 60-session correlation of daily implied-volatility changes across constituent pairs, ranked against its own prior three years. Stress is already a percentile; synchronisation becomes one. Each is split at 50 with a 45/55 band that holds its state in between, which gives four cells. [1]

CD, calm and dispersed: little is priced, and names move on their own. LS, localised stress: high stress without synchronisation, which may sit in a few names or be spread unevenly. SS, synchronised stress: stress across the market, repricing together. SC, synchronised calm: stress has receded from the prices while constituent movement remains aligned.

Few routes, taken regularly

The routes between the cells are few and regular. CD and LS trade places most often, 24 and 23 times over the eleven years. SS rarely returns straight to calm: it eased into SC in 24 of its 31 exits, and SC went back to SS in 20 of its 29. SC is the least settled cell: the stress has left the prices but not the co-movement. The only diagonal moves, where stress and synchronisation crossed on the same session, were CD to SS three times and LS to SC once.

Shares and spells over the window: CD 34% of sessions with a median spell of 19 sessions; LS 17% and 8; SS 35% and 18; SC 13% and 8. [1]

Where the vocabulary comes from

The terrain's language of recruitment and release comes from a branch of complexity science whose models produce events of every size without a trigger of matching size: growth connects patches, a spark spreads as far as the connections allow, and what burned changes the ground the next fire meets. We borrow that vocabulary for thinking about how names are recruited into common repricing and released from it. We do not test whether markets have that property, and nothing in the readings depends on it; the cells are named for mechanics, not for fire. [2] [3] Practitioners have read markets through the same lens, among them Convex Strategies. [4]

Fragility: how much more the skew steepens on falls than it flattens on rallies

The second reading asks how the surface responds to price shocks. For each session we fit, on data up to and including it, how much the cross-section's 25-delta put/call skew steepens per standardised index fall and how much it flattens per standardised index rally, each move measured in units of SPY's prior 21-session daily volatility, using a baseline-plus-impulse panel across the fifty names. The first is expression, E, the second repair, R, and fragility is H = E − R. Higher fragility means a stronger tilt towards downside expression relative to upside repair. Demand-driven option pricing offers one reason that tilt can persist; the measurement does not depend on it. [5]

Fragility is a relative reading. Each session's value is ranked against its prior 756 sessions (minimum 252) and labelled High above the 55th percentile, Low below the 45th, with the label held between. Fits carry forward between eligible updates, so persistence partly reflects measurement. Because the band is relative, High is common: 57% of sessions from January 2015 to December 2025, and every session of 2021. [1] A reader should keep that base rate in mind when a High reading is reported.

Fragility tracks no single index measure closely

The first question a desk asks is whether fragility is a relabelled index measure. Over 2,766 sessions its level is nearly uncorrelated with VIX and VIX3M, modestly correlated with VVIX, VIXEQ and DSPX, and negatively with COR1M. The one substantial overlap is SKEW, at 0.60, as expected of a skew-response measure, and that is where a rival explanation should start.

Spearman rank correlations of fragility against Cboe index closes, 2 January 2015 to 31 December 2025. The shares are the fraction of sessions on which fragility read High when the index sat in its own top prior-756-session quintile, and on all other sessions. [6] [1]

At the margin fragility does move with the volatility complex: 21-session changes correlate about 0.3 with changes in VIX, VIX3M, VVIX and COR1M. When an index sits in its own top prior quintile, fragility is no more likely to read High, except under VVIX and SKEW.

Why the two layers are read together

Terrain and fragility recover on different clocks. In 2025 the terrain had returned to calm by late July while the response of protection to index moves had not returned to its February state, so a reader of the index alone would have called the two dates alike (In 2025 the index recovered. The surface beneath it had not.). Combining the four cells with the fragility band gives eight descriptive cells; where each of them led over 2015–2025 is counted in the same study's second half.

How the readings are built

Terrain. Constituent IV stress is the index-weighted mean, over the point-in-time fifty largest names, of each name's 30-day implied volatility percentile against its own prior 756 sessions (at least 252), computed strictly before the session; a session needs at least 20 names and 90% of the basket's weight. Synchronisation is the equal-weighted mean, over all name pairs, of the 60-session correlation of daily implied-volatility changes, each change net of its own prior 252-session mean, with at least 57 joint observations; it is then ranked against its own prior 756 sessions (at least 252). Each axis reads high above 55 and low below 45 and holds its state in between. The cells are CD (both low), SC (synchronisation high, stress low), LS (stress high, synchronisation low) and SS (both high). [1]

Fragility. The skew is s = 100 · ln(P/C), the 25-delta put and call 30-day implied volatilities, and the response is its daily change. The move is z, SPY's log return divided by its 21-session realised daily volatility to the prior close; falls enter as max(−z, 0) and rallies as max(z, 0). A session enters the fit when at least 20 names respond, after trimming changes above 50 log points and moves above 10 standard deviations. On each such session a smooth baseline plus a sparse impulse is refitted across names on all data up to and including that session, after a 60-event warm-up, with smoothness and sparsity penalties fixed in advance. Expression E is the falls-side baseline and repair R minus the rallies-side baseline, each carried forward between its own fits, and fragility is H = E − R. H is ranked against its own prior 756 sessions (at least 252) and banded High above 55 and Low below 45, holding in between. [1]

Timing. Readings are formed at a session's close and published once the session is historical. The option inputs are a 15:46 ET quote snapshot; the fragility fit uses that session's closing SPY return. Response readings keep their last value between eligible updates, and 30-day implied volatility includes earnings effects.

Data, scope and limitations

Everything on this site is developed history from one dataset, read over 2 January 2015 to 31 December 2025, with earlier rows used only to warm up rankings and fits. It is not a holdout: every session had been examined before the definitions were settled, so a rule frozen today and run on new data is the test that has not yet been made. Terrain, fragility, the per-name 30-day constant-maturity implied volatility, closes, basket memberships and weights all come from one release of our data, and every input was checked against it by hash. [1]

The basket is the point-in-time top fifty of the US large-cap index, reconstructed from the index fund's historical holdings; monthly entry and exit rules can retain a name ranked just below fifty, and no survivor filter selects the basket. Missing names or pairs are excluded and denominators adjusted, subject to the coverage gates above. Two gaps are our own plumbing, not the market: our closes carry no prices for AGN and CELG, two basket names in 2014–2017, so their returns are missing from the terrain and 1,028 name-days inside the window leave the response fit, a defect logged for repair; and one control term of the response study is dropped because our spread data carry no expiry length. Nothing was back-filled. [1]

The transition and tail exhibits in the recovery study rest on small counts and dependent spells and carry no null test. All accounts are US large-cap; no other geography, basket or asset class has been run, and transfer is untested. Option marks are one 15:46 ET quote snapshot at mid, without fills. Synchronisation of implied-volatility changes is not return correlation; a fragility percentile is a rank against the reading's own history, not a probability.

Sources

[1] Altus Works. Data and methods notes, October 2026, available to reviewers on request: the point-in-time fifty largest constituents of the US large-cap index, 30-day constant-maturity implied volatility built from option quotes, adjusted closes, the terrain and fragility readings as published by the Altus terminal on 9 October 2026, and, for each exhibit, the protocol, code and checks behind it.

[2] Bak, P., Tang, C. and Wiesenfeld, K. "Self-organized criticality: An explanation of the 1/f noise." Physical Review Letters 59, 381–384 (1987), doi:10.1103/PhysRevLett.59.381; and "Self-organized criticality." Physical Review A 38, 364–374 (1988), doi:10.1103/PhysRevA.38.364.

[3] Drossel, B. and Schwabl, F. "Self-organized critical forest-fire model." Physical Review Letters 69, 1629–1632 (1992), doi:10.1103/PhysRevLett.69.1629; Palmieri, L. and Jensen, H. J. "The Forest Fire Model: The Subtleties of Criticality and Scale Invariance." Frontiers in Physics 8, 257 (2020), doi:10.3389/fphy.2020.00257.

[4] Convex Strategies (David Dredge, Chief Investment Officer). "Risk Update: August 2021 – Self-Organised Criticality," 22 September 2021. convex-strategies.com.

[5] Gârleanu, N., Pedersen, L. H. and Poteshman, A. M. "Demand-Based Option Pricing." Review of Financial Studies 22(10), 4259–4299 (2009). doi:10.1093/rfs/hhp005.

[6] Cboe Global Markets. Daily index histories, 2015–2025: VIX, VIX3M, VVIX, SKEW, VIXEQ, COR1M and DSPX. VIX historical data; COR1M history.